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QUESTIONS ON THE FUNDAMENTAL THEOREM OF CALCULUS TEST YOUR UNDERSTANDING OF INTEGRATION AND DIFFERENTIATION RELATIONSHIPS

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QUESTIONS ON THE FUNDAMENTAL THEOREM OF CALCULUS TEST YOUR
UNDERSTANDING OF INTEGRATION AND DIFFERENTIATION
RELATIONSHIPS
1. If f(x) = ∫₀ˣ (t² + 1) dt, then f'(x) =
a) x² b) x² + 1 c) 2x d) 3x² + 1
Answer: b) x² + 1
2. Given F(x) = ∫₀ˣ sin(t) dt, what is F'(x)?
a) cos(x) b) -sin(x) c) sin(x) d) -cos(x)
Answer: c) sin(x)
3. If g(x) = ∫₁ˣ e^t dt, then g'(x) =
a) e^x b) e c) xe^x d) e^(x-1)
Answer: a) e^x
4. Let h(x) = ∫₀ˣ √t dt. What is h'(x)?
a) 1/√x b) √x c) 2√x d) x^(3/2)
Answer: b) √x
5. If f(x) = ∫₂ˣ (1/t) dt, then f'(x) =
a) 1/x b) -1/x c) ln(x) d) 1/2
Answer: a) 1/x
6. Given F(x) = ∫₀ˣ cos(πt) dt, what is F'(x)?
a) -sin(πx) b) cos(πx) c) πsin(πx) d) -πcos(πx)
Answer: b) cos(πx)
7. If g(x) = ∫₁ˣ t³ dt, then g'(x) =
a) 3x² b) x³ c) x⁴ d) 4x³
Answer: b) x³
8. Let h(x) = ∫₀ˣ ln(t) dt. What is h'(x)?
a) 1/x b) ln(x) c) x ln(x) d) x/ln(x)
Answer: b) ln(x)
9. If f(x) = ∫₀ˣ (t² - 2t) dt, then f'(x) =
a) x² - 2x b) 2x - 2 c) x² - x d) 2x² - 2x
Answer: a) x² - 2x
10. Given F(x) = ∫₁ˣ (1/√t) dt, what is F'(x)?
a) √x b) 1/√x c) 2√x d) -1/√x
Answer: b) 1/√x
11. If g(x) = ∫₀ˣ tan(t) dt, then g'(x) =
a) sec²(x) b) tan(x) c) sin(x) d) cos(x)
Answer: b) tan(x)
12. Let h(x) = ∫₂ˣ (1/t²) dt. What is h'(x)?
a) -1/x² b) 1/x² c) -2/x³ d) 2/x³
Answer: a) -1/x²
13. If f(x) = ∫₀ˣ sec²(t) dt, then f'(x) =
a) tan(x) b) sec(x) c) sec²(x) d) sec(x)tan(x)
Answer: c) sec²(x)
14. Given F(x) = ∫₁ˣ (t + 1/t) dt, what is F'(x)?
a) x + 1/x b) 1 + 1/x² c) x - 1/x d) 1 - 1/x²
Answer: a) x + 1/x
15. If g(x) = ∫₀ˣ arcsin(t) dt, then g'(x) =
a) 1/√(1-x²) b) arcsin(x) c) cos(x) d) sin(x)
Answer: b) arcsin(x)
16. Let h(x) = ∫₁ˣ e^(-t²) dt. What is h'(x)?
a) -e^(-x²) b) e^(-x²) c) -2xe^(-x²) d) 2xe^(-x²)
Answer: b) e^(-x²)
17. If f(x) = ∫₀ˣ cosh(t) dt, then f'(x) =
a) sinh(x) b) cosh(x) c) tanh(x) d) sech(x)
Answer: b) cosh(x)
18. Given F(x) = ∫₀ˣ (1/(1+t²)) dt, what is F'(x)?
a) 1/(1+x²) b) 2x/(1+x²) c) arctan(x) d) -1/(1+x²)
Answer: a) 1/(1+x²)
19. If g(x) = ∫₂ˣ ln(t) dt, then g'(x) =
a) 1/x b) ln(2) c) ln(x) d) x ln(x)
Answer: c) ln(x)
20. Let h(x) = ∫₀ˣ √(1-t²) dt. What is h'(x)?
a) √(1-x²) b) -√(1-x²) c) 1/√(1-x²) d) -1/√(1-x²)
Answer: a) √(1-x²)
21. If f(x) = ∫₁ˣ (1/ln(t)) dt, then f'(x) =
a) 1/x b) 1/ln(x) c) ln(x)/x d) x/ln(x)
Answer: b) 1/ln(x)
22. Given F(x) = ∫₀ˣ arctan(t) dt, what is F'(x)?
a) 1/(1+x²) b) arctan(x) c) tan(x) d) sec²(x)
Answer: b) arctan(x)
23. If g(x) = ∫₀ˣ (sin(t)/t) dt, then g'(x) =
a) cos(x)/x b) sin(x)/x c) 1/x d) sin(x)
Answer: b) sin(x)/x
24. Let h(x) = ∫₁ˣ (t^n) dt, where n ≠ -1. What is h'(x)?
a) nx^(n-1) b) x^n c) x^(n+1) d) (n+1)x^n
Answer: b) x^n
25. If f(x) = ∫₀ˣ sec(t) dt, then f'(x) =
a) tan(x) b) sec(x) c) sec(x)tan(x) d) csc(x)
Answer: b) sec(x)
26. Given F(x) = ∫₀ˣ (e^t + e^(-t)) dt, what is F'(x)?
a) e^x - e^(-x) b) e^x + e^(-x) c) e^x d) e^(-x)
Answer: b) e^x + e^(-x)
27. If g(x) = ∫₁ˣ (1/√(t²-1)) dt, then g'(x) =
a) 1/√(x²-1) b) x/√(x²-1) c) 1/√(1-x²) d) x/√(1-x²)
Answer: a) 1/√(x²-1)
28. Let h(x) = ∫₀ˣ (t³ + 3t² + 3t + 1) dt. What is h'(x)?
a) 3x² + 6x + 3 b) x³ + 3x² + 3x + 1 c) 4x³ + 9x² + 6x + 1 d) x⁴ + x³ + x² + x
Answer: b) x³ + 3x² + 3x + 1
29. If f(x) = ∫₀ˣ sinh(t) dt, then f'(x) =
a) cosh(x) b) sinh(x) c) tanh(x) d) sech(x)
Answer: b) sinh(x)
30. Given F(x) = ∫₁ˣ (1/t²) dt, what is F'(x)?
a) -1/x² b) 1/x² c) -2/x³ d) 2/x³
Answer: a) -1/x²
31. If g(x) = ∫₀ˣ cos²(t) dt, then g'(x) =
a) sin(x)cos(x) b) cos²(x) c) -sin(x)cos(x) d) sin²(x)
Answer: b) cos²(x)
32. Let h(x) = ∫₀ˣ (1/√(1-t²)) dt. What is h'(x)?
a) 1/√(1-x²) b) -1/√(1-x²) c) √(1-x²) d) -√(1-x²)
Answer: a) 1/√(1-x²)
33. If f(x) = ∫₀ˣ (e^t / t) dt, then f'(x) =
a) e^x / x b) e^x c) 1/x d) e^x + 1/x
Answer: a) e^x / x
34. Given F(x) = ∫₀ˣ (t ln(t)) dt, what is F'(x)?
a) ln(x) b) x ln(x) c) x + ln(x) d) x ln(x) - x
Answer: b) x ln(x)
35. If g(x) = ∫₁ˣ (1/(1+t³)) dt, then g'(x) =
a) 1/(1+x³) b) 3x²/(1+x³) c) 1/(1+x) d) 3/(1+x³)
Answer: a) 1/(1+x³)
36. Let h(x) = ∫₀ˣ arccos(t) dt. What is h'(x)?
a) -1/√(1-x²) b) 1/√(1-x²) c) arccos(x) d) -arccos(x)
Answer: c) arccos(x)
37. If f(x) = ∫₀ˣ (t/(1+t²)) dt, then f'(x) =
a) 1/(1+x²) b) x/(1+x²) c) arctan(x) d) 2x/(1+x²)
Answer: b) x/(1+x²)
38. Given F(x) = ∫₀ˣ csc(t) dt, what is F'(x)?
a) sec(x) b) csc(x) c) cot(x) d) tan(x)
Answer: b) csc(x)
39. If g(x) = ∫₁ˣ (ln(t)/t) dt, then g'(x) =
a) ln(ln(x)) b) ln(x)/x c) 1/x d) ln²(x)/2
Answer: b) ln(x)/x
40. Let h(x) = ∫₀ˣ (1/(a²+t²)) dt, where a is a constant. What is h'(x)?
a) 1/(a²+x²) b) 2x/(a²+x²) c) a/(a²+x²) d) x/(a²+x²)
Answer: a) 1/(a²+x²)
41. If f(x) = ∫₀ˣ (1/√(1+t³)) dt, then f'(x) =
a) 1/√(1+x³) b) 3x²/√(1+x³) c) 1/(1+x³) d) 3/(1+x³)
Answer: a) 1/√(1+x³)
42. Given F(x) = ∫₀ˣ (t²e^t) dt, what is F'(x)?
a) x²e^x b) 2xe^x c) e^x d) x²e^x + 2xe^x
Answer: a) x²e^x
43. If g(x) = ∫₀ˣ (sin(t)/t²) dt, then g'(x) =
a) cos(x)/x² b) sin(x)/x² c) -sin(x)/x³ d) cos(x)/x
Answer: b) sin(x)/x²
44. Let h(x) = ∫₁ˣ (t ln²(t)) dt. What is h'(x)?
a) ln²(x) b) x ln²(x) c) 2x ln(x) d) 2 ln(x)
Answer: b) x ln²(x)
45. If f(x) = ∫₀ˣ (cos(t²)) dt, then f'(x) =
a) -2x sin(x²) b) cos(x²) c) -sin(x²) d) 2x cos(x²)
Answer: b) cos(x²)
46. Given F(x) = ∫₀ˣ (1/(1+e^t)) dt, what is F'(x)?
a) 1/(1+e^x) b) e^x/(1+e^x) c) 1/(1+e^(-x)) d) e^(-x)/(1+e^(-x))
Answer: a) 1/(1+e^x)
47. If g(x) = ∫₁ˣ (√(t²+1)) dt, then g'(x) =
a) √(x²+1) b) x/√(x²+1) c) 1/√(x²+1) d) x√(x²+1)
Answer: a) √(x²+1)
48. Let h(x) = ∫₀ˣ (t sin(t)) dt. What is h'(x)?
a) sin(x) b) x sin(x) c) cos(x) d) x cos(x)
Answer: b) x sin(x)
49. If f(x) = ∫₀ˣ (e^(-t²)) dt, then f'(x) =
a) -2xe^(-x²) b) e^(-x²) c) -e^(-x²) d) 2xe^(-x²)
Answer: b) e^(-x²)
. Given F(x) = ∫₀ˣ (t ln(t)) dt, what is F'(x)?
a) ln(x) b) x ln(x) c) x + ln(x) d) x ln(x) - x
Answer: b) x ln(x)
35. If g(x) = ∫₁ˣ (1/(1+t³)) dt, then g'(x) =
a) 1/(1+x³) b) 3x²/(1+x³) c) 1/(1+x) d) 3/(1+x³)
Answer: a) 1/(1+x³)
36. Let h(x) = ∫₀ˣ arccos(t) dt. What is h'(x)?
a) -1/√(1-x²) b) 1/√(1-x²) c) arccos(x) d) -arccos(x)
Answer: c) arccos(x)
37. If f(x) = ∫₀ˣ (t/(1+t²)) dt, then f'(x) =
a) 1/(1+x²) b) x/(1+x²) c) arctan(x) d) 2x/(1+x²)
Answer: b) x/(1+x²)
38. Given F(x) = ∫₀ˣ csc(t) dt, what is F'(x)?
a) sec(x) b) csc(x) c) cot(x) d) tan(x)
Answer: b) csc(x)
39. If g(x) = ∫₁ˣ (ln(t)/t) dt, then g'(x) =
a) ln(ln(x)) b) ln(x)/x c) 1/x d) ln²(x)/2
Answer: b) ln(x)/x
40. Let h(x) = ∫₀ˣ (1/(a²+t²)) dt, where a is a constant. What is h'(x)?
a) 1/(a²+x²) b) 2x/(a²+x²) c) a/(a²+x²) d) x/(a²+x²)
Answer: a) 1/(a²+x²)
41. If f(x) = ∫₀ˣ (1/√(1+t³)) dt, then f'(x) =
a) 1/√(1+x³) b) 3x²/√(1+x³) c) 1/(1+x³) d) 3/(1+x³)
Answer: a) 1/√(1+x³)
42. Given F(x) = ∫₀ˣ (t²e^t) dt, what is F'(x)?
a) x²e^x b) 2xe^x c) e^x d) x²e^x + 2xe^x
Answer: a) x²e^x
43. If g(x) = ∫₀ˣ (sin(t)/t²) dt, then g'(x) =
a) cos(x)/x² b) sin(x)/x² c) -sin(x)/x³ d) cos(x)/x
Answer: b) sin(x)/x²
44. Let h(x) = ∫₁ˣ (t ln²(t)) dt. What is h'(x)?
a) ln²(x) b) x ln²(x) c) 2x ln(x) d) 2 ln(x)
Answer: b) x ln²(x)
45. If f(x) = ∫₀ˣ (cos(t²)) dt, then f'(x) =
a) -2x sin(x²) b) cos(x²) c) -sin(x²) d) 2x cos(x²)
Answer: b) cos(x²)
46. Given F(x) = ∫₀ˣ (1/(1+e^t)) dt, what is F'(x)?
a) 1/(1+e^x) b) e^x/(1+e^x) c) 1/(1+e^(-x)) d) e^(-x)/(1+e^(-x))
Answer: a) 1/(1+e^x)
47. If g(x) = ∫₁ˣ (√(t²+1)) dt, then g'(x) =
a) √(x²+1) b) x/√(x²+1) c) 1/√(x²+1) d) x√(x²+1)
Answer: a) √(x²+1)
48. Let h(x) = ∫₀ˣ (t sin(t)) dt. What is h'(x)?
a) sin(x) b) x sin(x) c) cos(x) d) x cos(x)
Answer: b) x sin(x)
49. If f(x) = ∫₀ˣ (e^(-t²)) dt, then f'(x) =
a) -2xe^(-x²) b) e^(-x²) c) -e^(-x²) d) 2xe^(-x²)
Answer: b) e^(-x²)
. Given F(x) = ∫₀ˣ (t ln(t)) dt, what is F'(x)?
a) ln(x) b) x ln(x) c) x + ln(x) d) x ln(x) - x
Answer: b) x ln(x)
35. If g(x) = ∫₁ˣ (1/(1+t³)) dt, then g'(x) =
a) 1/(1+x³) b) 3x²/(1+x³) c) 1/(1+x) d) 3/(1+x³)
Answer: a) 1/(1+x³)
36. Let h(x) = ∫₀ˣ arccos(t) dt. What is h'(x)?
a) -1/√(1-x²) b) 1/√(1-x²) c) arccos(x) d) -arccos(x)
Answer: c) arccos(x)
37. If f(x) = ∫₀ˣ (t/(1+t²)) dt, then f'(x) =
a) 1/(1+x²) b) x/(1+x²) c) arctan(x) d) 2x/(1+x²)
Answer: b) x/(1+x²)
38. Given F(x) = ∫₀ˣ csc(t) dt, what is F'(x)?
a) sec(x) b) csc(x) c) cot(x) d) tan(x)
Answer: b) csc(x)
39. If g(x) = ∫₁ˣ (ln(t)/t) dt, then g'(x) =
a) ln(ln(x)) b) ln(x)/x c) 1/x d) ln²(x)/2
Answer: b) ln(x)/x
40. Let h(x) = ∫₀ˣ (1/(a²+t²)) dt, where a is a constant. What is h'(x)?
a) 1/(a²+x²) b) 2x/(a²+x²) c) a/(a²+x²) d) x/(a²+x²)
Answer: a) 1/(a²+x²)
41. If f(x) = ∫₀ˣ (1/√(1+t³)) dt, then f'(x) =
a) 1/√(1+x³) b) 3x²/√(1+x³) c) 1/(1+x³) d) 3/(1+x³)
Answer: a) 1/√(1+x³)
42. Given F(x) = ∫₀ˣ (t²e^t) dt, what is F'(x)?
a) x²e^x b) 2xe^x c) e^x d) x²e^x + 2xe^x
Answer: a) x²e^x
43. If g(x) = ∫₀ˣ (sin(t)/t²) dt, then g'(x) =
a) cos(x)/x² b) sin(x)/x² c) -sin(x)/x³ d) cos(x)/x
Answer: b) sin(x)/x²
44. Let h(x) = ∫₁ˣ (t ln²(t)) dt. What is h'(x)?
a) ln²(x) b) x ln²(x) c) 2x ln(x) d) 2 ln(x)
Answer: b) x ln²(x)
45. If f(x) = ∫₀ˣ (cos(t²)) dt, then f'(x) =
a) -2x sin(x²) b) cos(x²) c) -sin(x²) d) 2x cos(x²)
Answer: b) cos(x²)
46. Given F(x) = ∫₀ˣ (1/(1+e^t)) dt, what is F'(x)?
a) 1/(1+e^x) b) e^x/(1+e^x) c) 1/(1+e^(-x)) d) e^(-x)/(1+e^(-x))
Answer: a) 1/(1+e^x)
47. If g(x) = ∫₁ˣ (√(t²+1)) dt, then g'(x) =
a) √(x²+1) b) x/√(x²+1) c) 1/√(x²+1) d) x√(x²+1)
Answer: a) √(x²+1)
48. Let h(x) = ∫₀ˣ (t sin(t)) dt. What is h'(x)?
a) sin(x) b) x sin(x) c) cos(x) d) x cos(x)
Answer: b) x sin(x)
49. If f(x) = ∫₀ˣ (e^(-t²)) dt, then f'(x) =
a) -2xe^(-x²) b) e^(-x²) c) -e^(-x²) d) 2xe^(-x²)
Answer: b) e^(-x²)
. Given F(x) = ∫₀ˣ (t ln(t)) dt, what is F'(x)?
a) ln(x) b) x ln(x) c) x + ln(x) d) x ln(x) - x
Answer: b) x ln(x)
35. If g(x) = ∫₁ˣ (1/(1+t³)) dt, then g'(x) =
a) 1/(1+x³) b) 3x²/(1+x³) c) 1/(1+x) d) 3/(1+x³)
Answer: a) 1/(1+x³)
36. Let h(x) = ∫₀ˣ arccos(t) dt. What is h'(x)?
a) -1/√(1-x²) b) 1/√(1-x²) c) arccos(x) d) -arccos(x)
Answer: c) arccos(x)
37. If f(x) = ∫₀ˣ (t/(1+t²)) dt, then f'(x) =
a) 1/(1+x²) b) x/(1+x²) c) arctan(x) d) 2x/(1+x²)
Answer: b) x/(1+x²)
38. Given F(x) = ∫₀ˣ csc(t) dt, what is F'(x)?
a) sec(x) b) csc(x) c) cot(x) d) tan(x)
Answer: b) csc(x)
39. If g(x) = ∫₁ˣ (ln(t)/t) dt, then g'(x) =
a) ln(ln(x)) b) ln(x)/x c) 1/x d) ln²(x)/2
Answer: b) ln(x)/x
40. Let h(x) = ∫₀ˣ (1/(a²+t²)) dt, where a is a constant. What is h'(x)?
a) 1/(a²+x²) b) 2x/(a²+x²) c) a/(a²+x²) d) x/(a²+x²)
Answer: a) 1/(a²+x²)
41. If f(x) = ∫₀ˣ (1/√(1+t³)) dt, then f'(x) =
a) 1/√(1+x³) b) 3x²/√(1+x³) c) 1/(1+x³) d) 3/(1+x³)
Answer: a) 1/√(1+x³)
42. Given F(x) = ∫₀ˣ (t²e^t) dt, what is F'(x)?
a) x²e^x b) 2xe^x c) e^x d) x²e^x + 2xe^x
Answer: a) x²e^x
43. If g(x) = ∫₀ˣ (sin(t)/t²) dt, then g'(x) =
a) cos(x)/x² b) sin(x)/x² c) -sin(x)/x³ d) cos(x)/x
Answer: b) sin(x)/x²
44. Let h(x) = ∫₁ˣ (t ln²(t)) dt. What is h'(x)?
a) ln²(x) b) x ln²(x) c) 2x ln(x) d) 2 ln(x)
Answer: b) x ln²(x)
45. If f(x) = ∫₀ˣ (cos(t²)) dt, then f'(x) =
a) -2x sin(x²) b) cos(x²) c) -sin(x²) d) 2x cos(x²)
Answer: b) cos(x²)
46. Given F(x) = ∫₀ˣ (1/(1+e^t)) dt, what is F'(x)?
a) 1/(1+e^x) b) e^x/(1+e^x) c) 1/(1+e^(-x)) d) e^(-x)/(1+e^(-x))
Answer: a) 1/(1+e^x)
47. If g(x) = ∫₁ˣ (√(t²+1)) dt, then g'(x) =
a) √(x²+1) b) x/√(x²+1) c) 1/√(x²+1) d) x√(x²+1)
Answer: a) √(x²+1)
48. Let h(x) = ∫₀ˣ (t sin(t)) dt. What is h'(x)?
a) sin(x) b) x sin(x) c) cos(x) d) x cos(x)
Answer: b) x sin(x)
49. If f(x) = ∫₀ˣ (e^(-t²)) dt, then f'(x) =
a) -2xe^(-x²) b) e^(-x²) c) -e^(-x²) d) 2xe^(-x²)
Answer: b) e^(-x²)
. Given F(x) = ∫₀ˣ (t ln(t)) dt, what is F'(x)?
a) ln(x) b) x ln(x) c) x + ln(x) d) x ln(x) - x
Answer: b) x ln(x)
35. If g(x) = ∫₁ˣ (1/(1+t³)) dt, then g'(x) =
a) 1/(1+x³) b) 3x²/(1+x³) c) 1/(1+x) d) 3/(1+x³)
Answer: a) 1/(1+x³)
36. Let h(x) = ∫₀ˣ arccos(t) dt. What is h'(x)?
a) -1/√(1-x²) b) 1/√(1-x²) c) arccos(x) d) -arccos(x)
Answer: c) arccos(x)
37. If f(x) = ∫₀ˣ (t/(1+t²)) dt, then f'(x) =
a) 1/(1+x²) b) x/(1+x²) c) arctan(x) d) 2x/(1+x²)
Answer: b) x/(1+x²)
38. Given F(x) = ∫₀ˣ csc(t) dt, what is F'(x)?
a) sec(x) b) csc(x) c) cot(x) d) tan(x)
Answer: b) csc(x)
39. If g(x) = ∫₁ˣ (ln(t)/t) dt, then g'(x) =
a) ln(ln(x)) b) ln(x)/x c) 1/x d) ln²(x)/2
Answer: b) ln(x)/x
40. Let h(x) = ∫₀ˣ (1/(a²+t²)) dt, where a is a constant. What is h'(x)?
a) 1/(a²+x²) b) 2x/(a²+x²) c) a/(a²+x²) d) x/(a²+x²)
Answer: a) 1/(a²+x²)
41. If f(x) = ∫₀ˣ (1/√(1+t³)) dt, then f'(x) =
a) 1/√(1+x³) b) 3x²/√(1+x³) c) 1/(1+x³) d) 3/(1+x³)
Answer: a) 1/√(1+x³)
42. Given F(x) = ∫₀ˣ (t²e^t) dt, what is F'(x)?
a) x²e^x b) 2xe^x c) e^x d) x²e^x + 2xe^x
Answer: a) x²e^x
43. If g(x) = ∫₀ˣ (sin(t)/t²) dt, then g'(x) =
a) cos(x)/x² b) sin(x)/x² c) -sin(x)/x³ d) cos(x)/x
Answer: b) sin(x)/x²
44. Let h(x) = ∫₁ˣ (t ln²(t)) dt. What is h'(x)?
a) ln²(x) b) x ln²(x) c) 2x ln(x) d) 2 ln(x)
Answer: b) x ln²(x)
45. If f(x) = ∫₀ˣ (cos(t²)) dt, then f'(x) =
a) -2x sin(x²) b) cos(x²) c) -sin(x²) d) 2x cos(x²)
Answer: b) cos(x²)
46. Given F(x) = ∫₀ˣ (1/(1+e^t)) dt, what is F'(x)?
a) 1/(1+e^x) b) e^x/(1+e^x) c) 1/(1+e^(-x)) d) e^(-x)/(1+e^(-x))
Answer: a) 1/(1+e^x)
47. If g(x) = ∫₁ˣ (√(t²+1)) dt, then g'(x) =
a) √(x²+1) b) x/√(x²+1) c) 1/√(x²+1) d) x√(x²+1)
Answer: a) √(x²+1)
48. Let h(x) = ∫₀ˣ (t sin(t)) dt. What is h'(x)?
a) sin(x) b) x sin(x) c) cos(x) d) x cos(x)
Answer: b) x sin(x)
49. If f(x) = ∫₀ˣ (e^(-t²)) dt, then f'(x) =
a) -2xe^(-x²) b) e^(-x²) c) -e^(-x²) d) 2xe^(-x²)
Answer: b) e^(-x²)
. Given F(x) = ∫₀ˣ (t ln(t)) dt, what is F'(x)?
a) ln(x) b) x ln(x) c) x + ln(x) d) x ln(x) - x
Answer: b) x ln(x)
35. If g(x) = ∫₁ˣ (1/(1+t³)) dt, then g'(x) =
a) 1/(1+x³) b) 3x²/(1+x³) c) 1/(1+x) d) 3/(1+x³)
Answer: a) 1/(1+x³)
36. Let h(x) = ∫₀ˣ arccos(t) dt. What is h'(x)?
a) -1/√(1-x²) b) 1/√(1-x²) c) arccos(x) d) -arccos(x)
Answer: c) arccos(x)
37. If f(x) = ∫₀ˣ (t/(1+t²)) dt, then f'(x) =
a) 1/(1+x²) b) x/(1+x²) c) arctan(x) d) 2x/(1+x²)
Answer: b) x/(1+x²)
38. Given F(x) = ∫₀ˣ csc(t) dt, what is F'(x)?
a) sec(x) b) csc(x) c) cot(x) d) tan(x)
Answer: b) csc(x)
39. If g(x) = ∫₁ˣ (ln(t)/t) dt, then g'(x) =
a) ln(ln(x)) b) ln(x)/x c) 1/x d) ln²(x)/2
Answer: b) ln(x)/x
40. Let h(x) = ∫₀ˣ (1/(a²+t²)) dt, where a is a constant. What is h'(x)?
a) 1/(a²+x²) b) 2x/(a²+x²) c) a/(a²+x²) d) x/(a²+x²)
Answer: a) 1/(a²+x²)
41. If f(x) = ∫₀ˣ (1/√(1+t³)) dt, then f'(x) =
a) 1/√(1+x³) b) 3x²/√(1+x³) c) 1/(1+x³) d) 3/(1+x³)
Answer: a) 1/√(1+x³)
42. Given F(x) = ∫₀ˣ (t²e^t) dt, what is F'(x)?
a) x²e^x b) 2xe^x c) e^x d) x²e^x + 2xe^x
Answer: a) x²e^x
43. If g(x) = ∫₀ˣ (sin(t)/t²) dt, then g'(x) =
a) cos(x)/x² b) sin(x)/x² c) -sin(x)/x³ d) cos(x)/x
Answer: b) sin(x)/x²
44. Let h(x) = ∫₁ˣ (t ln²(t)) dt. What is h'(x)?
a) ln²(x) b) x ln²(x) c) 2x ln(x) d) 2 ln(x)
Answer: b) x ln²(x)
45. If f(x) = ∫₀ˣ (cos(t²)) dt, then f'(x) =
a) -2x sin(x²) b) cos(x²) c) -sin(x²) d) 2x cos(x²)
Answer: b) cos(x²)
46. Given F(x) = ∫₀ˣ (1/(1+e^t)) dt, what is F'(x)?
a) 1/(1+e^x) b) e^x/(1+e^x) c) 1/(1+e^(-x)) d) e^(-x)/(1+e^(-x))
Answer: a) 1/(1+e^x)
47. If g(x) = ∫₁ˣ (√(t²+1)) dt, then g'(x) =
a) √(x²+1) b) x/√(x²+1) c) 1/√(x²+1) d) x√(x²+1)
Answer: a) √(x²+1)
48. Let h(x) = ∫₀ˣ (t sin(t)) dt. What is h'(x)?
a) sin(x) b) x sin(x) c) cos(x) d) x cos(x)
Answer: b) x sin(x)
49. If f(x) = ∫₀ˣ (e^(-t²)) dt, then f'(x) =
a) -2xe^(-x²) b) e^(-x²) c) -e^(-x²) d) 2xe^(-x²)
Answer: b) e^(-x²)
. Given F(x) = ∫₀ˣ (t ln(t)) dt, what is F'(x)?
a) ln(x) b) x ln(x) c) x + ln(x) d) x ln(x) - x
Answer: b) x ln(x)
35. If g(x) = ∫₁ˣ (1/(1+t³)) dt, then g'(x) =
a) 1/(1+x³) b) 3x²/(1+x³) c) 1/(1+x) d) 3/(1+x³)
Answer: a) 1/(1+x³)
36. Let h(x) = ∫₀ˣ arccos(t) dt. What is h'(x)?
a) -1/√(1-x²) b) 1/√(1-x²) c) arccos(x) d) -arccos(x)
Answer: c) arccos(x)
37. If f(x) = ∫₀ˣ (t/(1+t²)) dt, then f'(x) =
a) 1/(1+x²) b) x/(1+x²) c) arctan(x) d) 2x/(1+x²)
Answer: b) x/(1+x²)
38. Given F(x) = ∫₀ˣ csc(t) dt, what is F'(x)?
a) sec(x) b) csc(x) c) cot(x) d) tan(x)
Answer: b) csc(x)
39. If g(x) = ∫₁ˣ (ln(t)/t) dt, then g'(x) =
a) ln(ln(x)) b) ln(x)/x c) 1/x d) ln²(x)/2
Answer: b) ln(x)/x
40. Let h(x) = ∫₀ˣ (1/(a²+t²)) dt, where a is a constant. What is h'(x)?
a) 1/(a²+x²) b) 2x/(a²+x²) c) a/(a²+x²) d) x/(a²+x²)
Answer: a) 1/(a²+x²)
41. If f(x) = ∫₀ˣ (1/√(1+t³)) dt, then f'(x) =
a) 1/√(1+x³) b) 3x²/√(1+x³) c) 1/(1+x³) d) 3/(1+x³)
Answer: a) 1/√(1+x³)
42. Given F(x) = ∫₀ˣ (t²e^t) dt, what is F'(x)?
a) x²e^x b) 2xe^x c) e^x d) x²e^x + 2xe^x
Answer: a) x²e^x
43. If g(x) = ∫₀ˣ (sin(t)/t²) dt, then g'(x) =
a) cos(x)/x² b) sin(x)/x² c) -sin(x)/x³ d) cos(x)/x
Answer: b) sin(x)/x²
44. Let h(x) = ∫₁ˣ (t ln²(t)) dt. What is h'(x)?
a) ln²(x) b) x ln²(x) c) 2x ln(x) d) 2 ln(x)
Answer: b) x ln²(x)
45. If f(x) = ∫₀ˣ (cos(t²)) dt, then f'(x) =
a) -2x sin(x²) b) cos(x²) c) -sin(x²) d) 2x cos(x²)
Answer: b) cos(x²)
46. Given F(x) = ∫₀ˣ (1/(1+e^t)) dt, what is F'(x)?
a) 1/(1+e^x) b) e^x/(1+e^x) c) 1/(1+e^(-x)) d) e^(-x)/(1+e^(-x))
Answer: a) 1/(1+e^x)
47. If g(x) = ∫₁ˣ (√(t²+1)) dt, then g'(x) =
a) √(x²+1) b) x/√(x²+1) c) 1/√(x²+1) d) x√(x²+1)
Answer: a) √(x²+1)
48. Let h(x) = ∫₀ˣ (t sin(t)) dt. What is h'(x)?
a) sin(x) b) x sin(x) c) cos(x) d) x cos(x)
Answer: b) x sin(x)
49. If f(x) = ∫₀ˣ (e^(-t²)) dt, then f'(x) =
a) -2xe^(-x²) b) e^(-x²) c) -e^(-x²) d) 2xe^(-x²)
Answer: b) e^(-x²)
. Given F(x) = ∫₀ˣ (t ln(t)) dt, what is F'(x)?
a) ln(x) b) x ln(x) c) x + ln(x) d) x ln(x) - x
Answer: b) x ln(x)
35. If g(x) = ∫₁ˣ (1/(1+t³)) dt, then g'(x) =
a) 1/(1+x³) b) 3x²/(1+x³) c) 1/(1+x) d) 3/(1+x³)
Answer: a) 1/(1+x³)
36. Let h(x) = ∫₀ˣ arccos(t) dt. What is h'(x)?
a) -1/√(1-x²) b) 1/√(1-x²) c) arccos(x) d) -arccos(x)
Answer: c) arccos(x)
37. If f(x) = ∫₀ˣ (t/(1+t²)) dt, then f'(x) =
a) 1/(1+x²) b) x/(1+x²) c) arctan(x) d) 2x/(1+x²)
Answer: b) x/(1+x²)
38. Given F(x) = ∫₀ˣ csc(t) dt, what is F'(x)?
a) sec(x) b) csc(x) c) cot(x) d) tan(x)
Answer: b) csc(x)
39. If g(x) = ∫₁ˣ (ln(t)/t) dt, then g'(x) =
a) ln(ln(x)) b) ln(x)/x c) 1/x d) ln²(x)/2
Answer: b) ln(x)/x
40. Let h(x) = ∫₀ˣ (1/(a²+t²)) dt, where a is a constant. What is h'(x)?
a) 1/(a²+x²) b) 2x/(a²+x²) c) a/(a²+x²) d) x/(a²+x²)
Answer: a) 1/(a²+x²)
41. If f(x) = ∫₀ˣ (1/√(1+t³)) dt, then f'(x) =
a) 1/√(1+x³) b) 3x²/√(1+x³) c) 1/(1+x³) d) 3/(1+x³)
Answer: a) 1/√(1+x³)
42. Given F(x) = ∫₀ˣ (t²e^t) dt, what is F'(x)?
a) x²e^x b) 2xe^x c) e^x d) x²e^x + 2xe^x
Answer: a) x²e^x
43. If g(x) = ∫₀ˣ (sin(t)/t²) dt, then g'(x) =
a) cos(x)/x² b) sin(x)/x² c) -sin(x)/x³ d) cos(x)/x
Answer: b) sin(x)/x²
44. Let h(x) = ∫₁ˣ (t ln²(t)) dt. What is h'(x)?
a) ln²(x) b) x ln²(x) c) 2x ln(x) d) 2 ln(x)
Answer: b) x ln²(x)
45. If f(x) = ∫₀ˣ (cos(t²)) dt, then f'(x) =
a) -2x sin(x²) b) cos(x²) c) -sin(x²) d) 2x cos(x²)
Answer: b) cos(x²)
46. Given F(x) = ∫₀ˣ (1/(1+e^t)) dt, what is F'(x)?
a) 1/(1+e^x) b) e^x/(1+e^x) c) 1/(1+e^(-x)) d) e^(-x)/(1+e^(-x))
Answer: a) 1/(1+e^x)
47. If g(x) = ∫₁ˣ (√(t²+1)) dt, then g'(x) =
a) √(x²+1) b) x/√(x²+1) c) 1/√(x²+1) d) x√(x²+1)
Answer: a) √(x²+1)
48. Let h(x) = ∫₀ˣ (t sin(t)) dt. What is h'(x)?
a) sin(x) b) x sin(x) c) cos(x) d) x cos(x)
Answer: b) x sin(x)
49. If f(x) = ∫₀ˣ (e^(-t²)) dt, then f'(x) =
a) -2xe^(-x²) b) e^(-x²) c) -e^(-x²) d) 2xe^(-x²)
Answer: b) e^(-x²)
. Given F(x) = ∫₀ˣ (t ln(t)) dt, what is F'(x)?
a) ln(x) b) x ln(x) c) x + ln(x) d) x ln(x) - x
Answer: b) x ln(x)
35. If g(x) = ∫₁ˣ (1/(1+t³)) dt, then g'(x) =
a) 1/(1+x³) b) 3x²/(1+x³) c) 1/(1+x) d) 3/(1+x³)
Answer: a) 1/(1+x³)
36. Let h(x) = ∫₀ˣ arccos(t) dt. What is h'(x)?
a) -1/√(1-x²) b) 1/√(1-x²) c) arccos(x) d) -arccos(x)
Answer: c) arccos(x)
37. If f(x) = ∫₀ˣ (t/(1+t²)) dt, then f'(x) =
a) 1/(1+x²) b) x/(1+x²) c) arctan(x) d) 2x/(1+x²)
Answer: b) x/(1+x²)
38. Given F(x) = ∫₀ˣ csc(t) dt, what is F'(x)?
a) sec(x) b) csc(x) c) cot(x) d) tan(x)
Answer: b) csc(x)
39. If g(x) = ∫₁ˣ (ln(t)/t) dt, then g'(x) =
a) ln(ln(x)) b) ln(x)/x c) 1/x d) ln²(x)/2
Answer: b) ln(x)/x
40. Let h(x) = ∫₀ˣ (1/(a²+t²)) dt, where a is a constant. What is h'(x)?
a) 1/(a²+x²) b) 2x/(a²+x²) c) a/(a²+x²) d) x/(a²+x²)
Answer: a) 1/(a²+x²)
41. If f(x) = ∫₀ˣ (1/√(1+t³)) dt, then f'(x) =
a) 1/√(1+x³) b) 3x²/√(1+x³) c) 1/(1+x³) d) 3/(1+x³)
Answer: a) 1/√(1+x³)
42. Given F(x) = ∫₀ˣ (t²e^t) dt, what is F'(x)?
a) x²e^x b) 2xe^x c) e^x d) x²e^x + 2xe^x
Answer: a) x²e^x
43. If g(x) = ∫₀ˣ (sin(t)/t²) dt, then g'(x) =
a) cos(x)/x² b) sin(x)/x² c) -sin(x)/x³ d) cos(x)/x
Answer: b) sin(x)/x²
44. Let h(x) = ∫₁ˣ (t ln²(t)) dt. What is h'(x)?
a) ln²(x) b) x ln²(x) c) 2x ln(x) d) 2 ln(x)
Answer: b) x ln²(x)
45. If f(x) = ∫₀ˣ (cos(t²)) dt, then f'(x) =
a) -2x sin(x²) b) cos(x²) c) -sin(x²) d) 2x cos(x²)
Answer: b) cos(x²)
46. Given F(x) = ∫₀ˣ (1/(1+e^t)) dt, what is F'(x)?
a) 1/(1+e^x) b) e^x/(1+e^x) c) 1/(1+e^(-x)) d) e^(-x)/(1+e^(-x))
Answer: a) 1/(1+e^x)
47. If g(x) = ∫₁ˣ (√(t²+1)) dt, then g'(x) =
a) √(x²+1) b) x/√(x²+1) c) 1/√(x²+1) d) x√(x²+1)
Answer: a) √(x²+1)
48. Let h(x) = ∫₀ˣ (t sin(t)) dt. What is h'(x)?
a) sin(x) b) x sin(x) c) cos(x) d) x cos(x)
Answer: b) x sin(x)
49. If f(x) = ∫₀ˣ (e^(-t²)) dt, then f'(x) =
a) -2xe^(-x²) b) e^(-x²) c) -e^(-x²) d) 2xe^(-x²)
Answer: b) e^(-x²)
. Given F(x) = ∫₀ˣ (t ln(t)) dt, what is F'(x)?
a) ln(x) b) x ln(x) c) x + ln(x) d) x ln(x) - x
Answer: b) x ln(x)
35. If g(x) = ∫₁ˣ (1/(1+t³)) dt, then g'(x) =
a) 1/(1+x³) b) 3x²/(1+x³) c) 1/(1+x) d) 3/(1+x³)
Answer: a) 1/(1+x³)
36. Let h(x) = ∫₀ˣ arccos(t) dt. What is h'(x)?
a) -1/√(1-x²) b) 1/√(1-x²) c) arccos(x) d) -arccos(x)
Answer: c) arccos(x)
37. If f(x) = ∫₀ˣ (t/(1+t²)) dt, then f'(x) =
a) 1/(1+x²) b) x/(1+x²) c) arctan(x) d) 2x/(1+x²)
Answer: b) x/(1+x²)
38. Given F(x) = ∫₀ˣ csc(t) dt, what is F'(x)?
a) sec(x) b) csc(x) c) cot(x) d) tan(x)
Answer: b) csc(x)
39. If g(x) = ∫₁ˣ (ln(t)/t) dt, then g'(x) =
a) ln(ln(x)) b) ln(x)/x c) 1/x d) ln²(x)/2
Answer: b) ln(x)/x
40. Let h(x) = ∫₀ˣ (1/(a²+t²)) dt, where a is a constant. What is h'(x)?
a) 1/(a²+x²) b) 2x/(a²+x²) c) a/(a²+x²) d) x/(a²+x²)
Answer: a) 1/(a²+x²)
41. If f(x) = ∫₀ˣ (1/√(1+t³)) dt, then f'(x) =
a) 1/√(1+x³) b) 3x²/√(1+x³) c) 1/(1+x³) d) 3/(1+x³)
Answer: a) 1/√(1+x³)
42. Given F(x) = ∫₀ˣ (t²e^t) dt, what is F'(x)?
a) x²e^x b) 2xe^x c) e^x d) x²e^x + 2xe^x
Answer: a) x²e^x
43. If g(x) = ∫₀ˣ (sin(t)/t²) dt, then g'(x) =
a) cos(x)/x² b) sin(x)/x² c) -sin(x)/x³ d) cos(x)/x
Answer: b) sin(x)/x²
44. Let h(x) = ∫₁ˣ (t ln²(t)) dt. What is h'(x)?
a) ln²(x) b) x ln²(x) c) 2x ln(x) d) 2 ln(x)
Answer: b) x ln²(x)
45. If f(x) = ∫₀ˣ (cos(t²)) dt, then f'(x) =
a) -2x sin(x²) b) cos(x²) c) -sin(x²) d) 2x cos(x²)
Answer: b) cos(x²)
46. Given F(x) = ∫₀ˣ (1/(1+e^t)) dt, what is F'(x)?
a) 1/(1+e^x) b) e^x/(1+e^x) c) 1/(1+e^(-x)) d) e^(-x)/(1+e^(-x))
Answer: a) 1/(1+e^x)
47. If g(x) = ∫₁ˣ (√(t²+1)) dt, then g'(x) =
a) √(x²+1) b) x/√(x²+1) c) 1/√(x²+1) d) x√(x²+1)
Answer: a) √(x²+1)
48. Let h(x) = ∫₀ˣ (t sin(t)) dt. What is h'(x)?
a) sin(x) b) x sin(x) c) cos(x) d) x cos(x)
Answer: b) x sin(x)
49. If f(x) = ∫₀ˣ (e^(-t²)) dt, then f'(x) =
a) -2xe^(-x²) b) e^(-x²) c) -e^(-x²) d) 2xe^(-x²)
Answer: b) e^(-x²)
. Given F(x) = ∫₀ˣ (t ln(t)) dt, what is F'(x)?
a) ln(x) b) x ln(x) c) x + ln(x) d) x ln(x) - x
Answer: b) x ln(x)
35. If g(x) = ∫₁ˣ (1/(1+t³)) dt, then g'(x) =
a) 1/(1+x³) b) 3x²/(1+x³) c) 1/(1+x) d) 3/(1+x³)
Answer: a) 1/(1+x³)
36. Let h(x) = ∫₀ˣ arccos(t) dt. What is h'(x)?
a) -1/√(1-x²) b) 1/√(1-x²) c) arccos(x) d) -arccos(x)
Answer: c) arccos(x)
37. If f(x) = ∫₀ˣ (t/(1+t²)) dt, then f'(x) =
a) 1/(1+x²) b) x/(1+x²) c) arctan(x) d) 2x/(1+x²)
Answer: b) x/(1+x²)
38. Given F(x) = ∫₀ˣ csc(t) dt, what is F'(x)?
a) sec(x) b) csc(x) c) cot(x) d) tan(x)
Answer: b) csc(x)
39. If g(x) = ∫₁ˣ (ln(t)/t) dt, then g'(x) =
a) ln(ln(x)) b) ln(x)/x c) 1/x d) ln²(x)/2
Answer: b) ln(x)/x
40. Let h(x) = ∫₀ˣ (1/(a²+t²)) dt, where a is a constant. What is h'(x)?
a) 1/(a²+x²) b) 2x/(a²+x²) c) a/(a²+x²) d) x/(a²+x²)
Answer: a) 1/(a²+x²)
41. If f(x) = ∫₀ˣ (1/√(1+t³)) dt, then f'(x) =
a) 1/√(1+x³) b) 3x²/√(1+x³) c) 1/(1+x³) d) 3/(1+x³)
Answer: a) 1/√(1+x³)
42. Given F(x) = ∫₀ˣ (t²e^t) dt, what is F'(x)?
a) x²e^x b) 2xe^x c) e^x d) x²e^x + 2xe^x
Answer: a) x²e^x
43. If g(x) = ∫₀ˣ (sin(t)/t²) dt, then g'(x) =
a) cos(x)/x² b) sin(x)/x² c) -sin(x)/x³ d) cos(x)/x
Answer: b) sin(x)/x²
44. Let h(x) = ∫₁ˣ (t ln²(t)) dt. What is h'(x)?
a) ln²(x) b) x ln²(x) c) 2x ln(x) d) 2 ln(x)
Answer: b) x ln²(x)
45. If f(x) = ∫₀ˣ (cos(t²)) dt, then f'(x) =
a) -2x sin(x²) b) cos(x²) c) -sin(x²) d) 2x cos(x²)
Answer: b) cos(x²)
46. Given F(x) = ∫₀ˣ (1/(1+e^t)) dt, what is F'(x)?
a) 1/(1+e^x) b) e^x/(1+e^x) c) 1/(1+e^(-x)) d) e^(-x)/(1+e^(-x))
Answer: a) 1/(1+e^x)
47. If g(x) = ∫₁ˣ (√(t²+1)) dt, then g'(x) =
a) √(x²+1) b) x/√(x²+1) c) 1/√(x²+1) d) x√(x²+1)
Answer: a) √(x²+1)
48. Let h(x) = ∫₀ˣ (t sin(t)) dt. What is h'(x)?
a) sin(x) b) x sin(x) c) cos(x) d) x cos(x)
Answer: b) x sin(x)
49. If f(x) = ∫₀ˣ (e^(-t²)) dt, then f'(x) =
a) -2xe^(-x²) b) e^(-x²) c) -e^(-x²) d) 2xe^(-x²)
Answer: b) e^(-x²)
. Given F(x) = ∫₀ˣ (t ln(t)) dt, what is F'(x)?
a) ln(x) b) x ln(x) c) x + ln(x) d) x ln(x) - x
Answer: b) x ln(x)
35. If g(x) = ∫₁ˣ (1/(1+t³)) dt, then g'(x) =
a) 1/(1+x³) b) 3x²/(1+x³) c) 1/(1+x) d) 3/(1+x³)
Answer: a) 1/(1+x³)
36. Let h(x) = ∫₀ˣ arccos(t) dt. What is h'(x)?
a) -1/√(1-x²) b) 1/√(1-x²) c) arccos(x) d) -arccos(x)
Answer: c) arccos(x)
37. If f(x) = ∫₀ˣ (t/(1+t²)) dt, then f'(x) =
a) 1/(1+x²) b) x/(1+x²) c) arctan(x) d) 2x/(1+x²)
Answer: b) x/(1+x²)
38. Given F(x) = ∫₀ˣ csc(t) dt, what is F'(x)?
a) sec(x) b) csc(x) c) cot(x) d) tan(x)
Answer: b) csc(x)
39. If g(x) = ∫₁ˣ (ln(t)/t) dt, then g'(x) =
a) ln(ln(x)) b) ln(x)/x c) 1/x d) ln²(x)/2
Answer: b) ln(x)/x
40. Let h(x) = ∫₀ˣ (1/(a²+t²)) dt, where a is a constant. What is h'(x)?
a) 1/(a²+x²) b) 2x/(a²+x²) c) a/(a²+x²) d) x/(a²+x²)
Answer: a) 1/(a²+x²)
41. If f(x) = ∫₀ˣ (1/√(1+t³)) dt, then f'(x) =
a) 1/√(1+x³) b) 3x²/√(1+x³) c) 1/(1+x³) d) 3/(1+x³)
Answer: a) 1/√(1+x³)
42. Given F(x) = ∫₀ˣ (t²e^t) dt, what is F'(x)?
a) x²e^x b) 2xe^x c) e^x d) x²e^x + 2xe^x
Answer: a) x²e^x
43. If g(x) = ∫₀ˣ (sin(t)/t²) dt, then g'(x) =
a) cos(x)/x² b) sin(x)/x² c) -sin(x)/x³ d) cos(x)/x
Answer: b) sin(x)/x²
44. Let h(x) = ∫₁ˣ (t ln²(t)) dt. What is h'(x)?
a) ln²(x) b) x ln²(x) c) 2x ln(x) d) 2 ln(x)
Answer: b) x ln²(x)
45. If f(x) = ∫₀ˣ (cos(t²)) dt, then f'(x) =
a) -2x sin(x²) b) cos(x²) c) -sin(x²) d) 2x cos(x²)
Answer: b) cos(x²)
46. Given F(x) = ∫₀ˣ (1/(1+e^t)) dt, what is F'(x)?
a) 1/(1+e^x) b) e^x/(1+e^x) c) 1/(1+e^(-x)) d) e^(-x)/(1+e^(-x))
Answer: a) 1/(1+e^x)
47. If g(x) = ∫₁ˣ (√(t²+1)) dt, then g'(x) =
a) √(x²+1) b) x/√(x²+1) c) 1/√(x²+1) d) x√(x²+1)
Answer: a) √(x²+1)
48. Let h(x) = ∫₀ˣ (t sin(t)) dt. What is h'(x)?
a) sin(x) b) x sin(x) c) cos(x) d) x cos(x)
Answer: b) x sin(x)
49. If f(x) = ∫₀ˣ (e^(-t²)) dt, then f'(x) =
a) -2xe^(-x²) b) e^(-x²) c) -e^(-x²) d) 2xe^(-x²)
Answer: b) e^(-x²)
. Given F(x) = ∫₀ˣ (t ln(t)) dt, what is F'(x)?
a) ln(x) b) x ln(x) c) x + ln(x) d) x ln(x) - x
Answer: b) x ln(x)
35. If g(x) = ∫₁ˣ (1/(1+t³)) dt, then g'(x) =
a) 1/(1+x³) b) 3x²/(1+x³) c) 1/(1+x) d) 3/(1+x³)
Answer: a) 1/(1+x³)
36. Let h(x) = ∫₀ˣ arccos(t) dt. What is h'(x)?
a) -1/√(1-x²) b) 1/√(1-x²) c) arccos(x) d) -arccos(x)
Answer: c) arccos(x)
37. If f(x) = ∫₀ˣ (t/(1+t²)) dt, then f'(x) =
a) 1/(1+x²) b) x/(1+x²) c) arctan(x) d) 2x/(1+x²)
Answer: b) x/(1+x²)
38. Given F(x) = ∫₀ˣ csc(t) dt, what is F'(x)?
a) sec(x) b) csc(x) c) cot(x) d) tan(x)
Answer: b) csc(x)
39. If g(x) = ∫₁ˣ (ln(t)/t) dt, then g'(x) =
a) ln(ln(x)) b) ln(x)/x c) 1/x d) ln²(x)/2
Answer: b) ln(x)/x
40. Let h(x) = ∫₀ˣ (1/(a²+t²)) dt, where a is a constant. What is h'(x)?
a) 1/(a²+x²) b) 2x/(a²+x²) c) a/(a²+x²) d) x/(a²+x²)
Answer: a) 1/(a²+x²)
41. If f(x) = ∫₀ˣ (1/√(1+t³)) dt, then f'(x) =
a) 1/√(1+x³) b) 3x²/√(1+x³) c) 1/(1+x³) d) 3/(1+x³)
Answer: a) 1/√(1+x³)
42. Given F(x) = ∫₀ˣ (t²e^t) dt, what is F'(x)?
a) x²e^x b) 2xe^x c) e^x d) x²e^x + 2xe^x
Answer: a) x²e^x
43. If g(x) = ∫₀ˣ (sin(t)/t²) dt, then g'(x) =
a) cos(x)/x² b) sin(x)/x² c) -sin(x)/x³ d) cos(x)/x
Answer: b) sin(x)/x²
44. Let h(x) = ∫₁ˣ (t ln²(t)) dt. What is h'(x)?
a) ln²(x) b) x ln²(x) c) 2x ln(x) d) 2 ln(x)
Answer: b) x ln²(x)
45. If f(x) = ∫₀ˣ (cos(t²)) dt, then f'(x) =
a) -2x sin(x²) b) cos(x²) c) -sin(x²) d) 2x cos(x²)
Answer: b) cos(x²)
46. Given F(x) = ∫₀ˣ (1/(1+e^t)) dt, what is F'(x)?
a) 1/(1+e^x) b) e^x/(1+e^x) c) 1/(1+e^(-x)) d) e^(-x)/(1+e^(-x))
Answer: a) 1/(1+e^x)
47. If g(x) = ∫₁ˣ (√(t²+1)) dt, then g'(x) =
a) √(x²+1) b) x/√(x²+1) c) 1/√(x²+1) d) x√(x²+1)
Answer: a) √(x²+1)
48. Let h(x) = ∫₀ˣ (t sin(t)) dt. What is h'(x)?
a) sin(x) b) x sin(x) c) cos(x) d) x cos(x)
Answer: b) x sin(x)
49. If f(x) = ∫₀ˣ (e^(-t²)) dt, then f'(x) =
a) -2xe^(-x²) b) e^(-x²) c) -e^(-x²) d) 2xe^(-x²)
Answer: b) e^(-x²)
. Given F(x) = ∫₀ˣ (t ln(t)) dt, what is F'(x)?
a) ln(x) b) x ln(x) c) x + ln(x) d) x ln(x) - x
Answer: b) x ln(x)
35. If g(x) = ∫₁ˣ (1/(1+t³)) dt, then g'(x) =
a) 1/(1+x³) b) 3x²/(1+x³) c) 1/(1+x) d) 3/(1+x³)
Answer: a) 1/(1+x³)
36. Let h(x) = ∫₀ˣ arccos(t) dt. What is h'(x)?
a) -1/√(1-x²) b) 1/√(1-x²) c) arccos(x) d) -arccos(x)
Answer: c) arccos(x)
37. If f(x) = ∫₀ˣ (t/(1+t²)) dt, then f'(x) =
a) 1/(1+x²) b) x/(1+x²) c) arctan(x) d) 2x/(1+x²)
Answer: b) x/(1+x²)
38. Given F(x) = ∫₀ˣ csc(t) dt, what is F'(x)?
a) sec(x) b) csc(x) c) cot(x) d) tan(x)
Answer: b) csc(x)
39. If g(x) = ∫₁ˣ (ln(t)/t) dt, then g'(x) =
a) ln(ln(x)) b) ln(x)/x c) 1/x d) ln²(x)/2
Answer: b) ln(x)/x
40. Let h(x) = ∫₀ˣ (1/(a²+t²)) dt, where a is a constant. What is h'(x)?
a) 1/(a²+x²) b) 2x/(a²+x²) c) a/(a²+x²) d) x/(a²+x²)
Answer: a) 1/(a²+x²)
41. If f(x) = ∫₀ˣ (1/√(1+t³)) dt, then f'(x) =
a) 1/√(1+x³) b) 3x²/√(1+x³) c) 1/(1+x³) d) 3/(1+x³)
Answer: a) 1/√(1+x³)
42. Given F(x) = ∫₀ˣ (t²e^t) dt, what is F'(x)?
a) x²e^x b) 2xe^x c) e^x d) x²e^x + 2xe^x
Answer: a) x²e^x
43. If g(x) = ∫₀ˣ (sin(t)/t²) dt, then g'(x) =
a) cos(x)/x² b) sin(x)/x² c) -sin(x)/x³ d) cos(x)/x
Answer: b) sin(x)/x²
44. Let h(x) = ∫₁ˣ (t ln²(t)) dt. What is h'(x)?
a) ln²(x) b) x ln²(x) c) 2x ln(x) d) 2 ln(x)
Answer: b) x ln²(x)
45. If f(x) = ∫₀ˣ (cos(t²)) dt, then f'(x) =
a) -2x sin(x²) b) cos(x²) c) -sin(x²) d) 2x cos(x²)
Answer: b) cos(x²)
46. Given F(x) = ∫₀ˣ (1/(1+e^t)) dt, what is F'(x)?
a) 1/(1+e^x) b) e^x/(1+e^x) c) 1/(1+e^(-x)) d) e^(-x)/(1+e^(-x))
Answer: a) 1/(1+e^x)
47. If g(x) = ∫₁ˣ (√(t²+1)) dt, then g'(x) =
a) √(x²+1) b) x/√(x²+1) c) 1/√(x²+1) d) x√(x²+1)
Answer: a) √(x²+1)
48. Let h(x) = ∫₀ˣ (t sin(t)) dt. What is h'(x)?
a) sin(x) b) x sin(x) c) cos(x) d) x cos(x)
Answer: b) x sin(x)
49. If f(x) = ∫₀ˣ (e^(-t²)) dt, then f'(x) =
a) -2xe^(-x²) b) e^(-x²) c) -e^(-x²) d) 2xe^(-x²)
Answer: b) e^(-x²)
. Given F(x) = ∫₀ˣ (t ln(t)) dt, what is F'(x)?
a) ln(x) b) x ln(x) c) x + ln(x) d) x ln(x) - x
Answer: b) x ln(x)
35. If g(x) = ∫₁ˣ (1/(1+t³)) dt, then g'(x) =
a) 1/(1+x³) b) 3x²/(1+x³) c) 1/(1+x) d) 3/(1+x³)
Answer: a) 1/(1+x³)
36. Let h(x) = ∫₀ˣ arccos(t) dt. What is h'(x)?
a) -1/√(1-x²) b) 1/√(1-x²) c) arccos(x) d) -arccos(x)
Answer: c) arccos(x)
37. If f(x) = ∫₀ˣ (t/(1+t²)) dt, then f'(x) =
a) 1/(1+x²) b) x/(1+x²) c) arctan(x) d) 2x/(1+x²)
Answer: b) x/(1+x²)
38. Given F(x) = ∫₀ˣ csc(t) dt, what is F'(x)?
a) sec(x) b) csc(x) c) cot(x) d) tan(x)
Answer: b) csc(x)
39. If g(x) = ∫₁ˣ (ln(t)/t) dt, then g'(x) =
a) ln(ln(x)) b) ln(x)/x c) 1/x d) ln²(x)/2
Answer: b) ln(x)/x
40. Let h(x) = ∫₀ˣ (1/(a²+t²)) dt, where a is a constant. What is h'(x)?
a) 1/(a²+x²) b) 2x/(a²+x²) c) a/(a²+x²) d) x/(a²+x²)
Answer: a) 1/(a²+x²)
41. If f(x) = ∫₀ˣ (1/√(1+t³)) dt, then f'(x) =
a) 1/√(1+x³) b) 3x²/√(1+x³) c) 1/(1+x³) d) 3/(1+x³)
Answer: a) 1/√(1+x³)
42. Given F(x) = ∫₀ˣ (t²e^t) dt, what is F'(x)?
a) x²e^x b) 2xe^x c) e^x d) x²e^x + 2xe^x
Answer: a) x²e^x
43. If g(x) = ∫₀ˣ (sin(t)/t²) dt, then g'(x) =
a) cos(x)/x² b) sin(x)/x² c) -sin(x)/x³ d) cos(x)/x
Answer: b) sin(x)/x²
44. Let h(x) = ∫₁ˣ (t ln²(t)) dt. What is h'(x)?
a) ln²(x) b) x ln²(x) c) 2x ln(x) d) 2 ln(x)
Answer: b) x ln²(x)
45. If f(x) = ∫₀ˣ (cos(t²)) dt, then f'(x) =
a) -2x sin(x²) b) cos(x²) c) -sin(x²) d) 2x cos(x²)
Answer: b) cos(x²)
46. Given F(x) = ∫₀ˣ (1/(1+e^t)) dt, what is F'(x)?
a) 1/(1+e^x) b) e^x/(1+e^x) c) 1/(1+e^(-x)) d) e^(-x)/(1+e^(-x))
Answer: a) 1/(1+e^x)
47. If g(x) = ∫₁ˣ (√(t²+1)) dt, then g'(x) =
a) √(x²+1) b) x/√(x²+1) c) 1/√(x²+1) d) x√(x²+1)
Answer: a) √(x²+1)
48. Let h(x) = ∫₀ˣ (t sin(t)) dt. What is h'(x)?
a) sin(x) b) x sin(x) c) cos(x) d) x cos(x)
Answer: b) x sin(x)
49. If f(x) = ∫₀ˣ (e^(-t²)) dt, then f'(x) =
a) -2xe^(-x²) b) e^(-x²) c) -e^(-x²) d) 2xe^(-x²)
Answer: b) e^(-x²)
. Given F(x) = ∫₀ˣ (t ln(t)) dt, what is F'(x)?
a) ln(x) b) x ln(x) c) x + ln(x) d) x ln(x) - x
Answer: b) x ln(x)
35. If g(x) = ∫₁ˣ (1/(1+t³)) dt, then g'(x) =
a) 1/(1+x³) b) 3x²/(1+x³) c) 1/(1+x) d) 3/(1+x³)
Answer: a) 1/(1+x³)
36. Let h(x) = ∫₀ˣ arccos(t) dt. What is h'(x)?
a) -1/√(1-x²) b) 1/√(1-x²) c) arccos(x) d) -arccos(x)
Answer: c) arccos(x)
37. If f(x) = ∫₀ˣ (t/(1+t²)) dt, then f'(x) =
a) 1/(1+x²) b) x/(1+x²) c) arctan(x) d) 2x/(1+x²)
Answer: b) x/(1+x²)
38. Given F(x) = ∫₀ˣ csc(t) dt, what is F'(x)?
a) sec(x) b) csc(x) c) cot(x) d) tan(x)
Answer: b) csc(x)
39. If g(x) = ∫₁ˣ (ln(t)/t) dt, then g'(x) =
a) ln(ln(x)) b) ln(x)/x c) 1/x d) ln²(x)/2
Answer: b) ln(x)/x
40. Let h(x) = ∫₀ˣ (1/(a²+t²)) dt, where a is a constant. What is h'(x)?
a) 1/(a²+x²) b) 2x/(a²+x²) c) a/(a²+x²) d) x/(a²+x²)
Answer: a) 1/(a²+x²)
41. If f(x) = ∫₀ˣ (1/√(1+t³)) dt, then f'(x) =
a) 1/√(1+x³) b) 3x²/√(1+x³) c) 1/(1+x³) d) 3/(1+x³)
Answer: a) 1/√(1+x³)
42. Given F(x) = ∫₀ˣ (t²e^t) dt, what is F'(x)?
a) x²e^x b) 2xe^x c) e^x d) x²e^x + 2xe^x
Answer: a) x²e^x
43. If g(x) = ∫₀ˣ (sin(t)/t²) dt, then g'(x) =
a) cos(x)/x² b) sin(x)/x² c) -sin(x)/x³ d) cos(x)/x
Answer: b) sin(x)/x²
44. Let h(x) = ∫₁ˣ (t ln²(t)) dt. What is h'(x)?
a) ln²(x) b) x ln²(x) c) 2x ln(x) d) 2 ln(x)
Answer: b) x ln²(x)
45. If f(x) = ∫₀ˣ (cos(t²)) dt, then f'(x) =
a) -2x sin(x²) b) cos(x²) c) -sin(x²) d) 2x cos(x²)
Answer: b) cos(x²)
46. Given F(x) = ∫₀ˣ (1/(1+e^t)) dt, what is F'(x)?
a) 1/(1+e^x) b) e^x/(1+e^x) c) 1/(1+e^(-x)) d) e^(-x)/(1+e^(-x))
Answer: a) 1/(1+e^x)
47. If g(x) = ∫₁ˣ (√(t²+1)) dt, then g'(x) =
a) √(x²+1) b) x/√(x²+1) c) 1/√(x²+1) d) x√(x²+1)
Answer: a) √(x²+1)
48. Let h(x) = ∫₀ˣ (t sin(t)) dt. What is h'(x)?
a) sin(x) b) x sin(x) c) cos(x) d) x cos(x)
Answer: b) x sin(x)
49. If f(x) = ∫₀ˣ (e^(-t²)) dt, then f'(x) =
a) -2xe^(-x²) b) e^(-x²) c) -e^(-x²) d) 2xe^(-x²)
Answer: b) e^(-x²)
. Given F(x) = ∫₀ˣ (t ln(t)) dt, what is F'(x)?
a) ln(x) b) x ln(x) c) x + ln(x) d) x ln(x) - x
Answer: b) x ln(x)
35. If g(x) = ∫₁ˣ (1/(1+t³)) dt, then g'(x) =
a) 1/(1+x³) b) 3x²/(1+x³) c) 1/(1+x) d) 3/(1+x³)
Answer: a) 1/(1+x³)
36. Let h(x) = ∫₀ˣ arccos(t) dt. What is h'(x)?
a) -1/√(1-x²) b) 1/√(1-x²) c) arccos(x) d) -arccos(x)
Answer: c) arccos(x)
37. If f(x) = ∫₀ˣ (t/(1+t²)) dt, then f'(x) =
a) 1/(1+x²) b) x/(1+x²) c) arctan(x) d) 2x/(1+x²)
Answer: b) x/(1+x²)
38. Given F(x) = ∫₀ˣ csc(t) dt, what is F'(x)?
a) sec(x) b) csc(x) c) cot(x) d) tan(x)
Answer: b) csc(x)
39. If g(x) = ∫₁ˣ (ln(t)/t) dt, then g'(x) =
a) ln(ln(x)) b) ln(x)/x c) 1/x d) ln²(x)/2
Answer: b) ln(x)/x
40. Let h(x) = ∫₀ˣ (1/(a²+t²)) dt, where a is a constant. What is h'(x)?
a) 1/(a²+x²) b) 2x/(a²+x²) c) a/(a²+x²) d) x/(a²+x²)
Answer: a) 1/(a²+x²)
41. If f(x) = ∫₀ˣ (1/√(1+t³)) dt, then f'(x) =
a) 1/√(1+x³) b) 3x²/√(1+x³) c) 1/(1+x³) d) 3/(1+x³)
Answer: a) 1/√(1+x³)
42. Given F(x) = ∫₀ˣ (t²e^t) dt, what is F'(x)?
a) x²e^x b) 2xe^x c) e^x d) x²e^x + 2xe^x
Answer: a) x²e^x
43. If g(x) = ∫₀ˣ (sin(t)/t²) dt, then g'(x) =
a) cos(x)/x² b) sin(x)/x² c) -sin(x)/x³ d) cos(x)/x
Answer: b) sin(x)/x²
44. Let h(x) = ∫₁ˣ (t ln²(t)) dt. What is h'(x)?
a) ln²(x) b) x ln²(x) c) 2x ln(x) d) 2 ln(x)
Answer: b) x ln²(x)
45. If f(x) = ∫₀ˣ (cos(t²)) dt, then f'(x) =
a) -2x sin(x²) b) cos(x²) c) -sin(x²) d) 2x cos(x²)
Answer: b) cos(x²)
46. Given F(x) = ∫₀ˣ (1/(1+e^t)) dt, what is F'(x)?
a) 1/(1+e^x) b) e^x/(1+e^x) c) 1/(1+e^(-x)) d) e^(-x)/(1+e^(-x))
Answer: a) 1/(1+e^x)
47. If g(x) = ∫₁ˣ (√(t²+1)) dt, then g'(x) =
a) √(x²+1) b) x/√(x²+1) c) 1/√(x²+1) d) x√(x²+1)
Answer: a) √(x²+1)
48. Let h(x) = ∫₀ˣ (t sin(t)) dt. What is h'(x)?
a) sin(x) b) x sin(x) c) cos(x) d) x cos(x)
Answer: b) x sin(x)
49. If f(x) = ∫₀ˣ (e^(-t²)) dt, then f'(x) =
a) -2xe^(-x²) b) e^(-x²) c) -e^(-x²) d) 2xe^(-x²)
Answer: b) e^(-x²)
. Given F(x) = ∫₀ˣ (t ln(t)) dt, what is F'(x)?
a) ln(x) b) x ln(x) c) x + ln(x) d) x ln(x) - x
Answer: b) x ln(x)
35. If g(x) = ∫₁ˣ (1/(1+t³)) dt, then g'(x) =
a) 1/(1+x³) b) 3x²/(1+x³) c) 1/(1+x) d) 3/(1+x³)
Answer: a) 1/(1+x³)
36. Let h(x) = ∫₀ˣ arccos(t) dt. What is h'(x)?
a) -1/√(1-x²) b) 1/√(1-x²) c) arccos(x) d) -arccos(x)
Answer: c) arccos(x)
37. If f(x) = ∫₀ˣ (t/(1+t²)) dt, then f'(x) =
a) 1/(1+x²) b) x/(1+x²) c) arctan(x) d) 2x/(1+x²)
Answer: b) x/(1+x²)
38. Given F(x) = ∫₀ˣ csc(t) dt, what is F'(x)?
a) sec(x) b) csc(x) c) cot(x) d) tan(x)
Answer: b) csc(x)
39. If g(x) = ∫₁ˣ (ln(t)/t) dt, then g'(x) =
a) ln(ln(x)) b) ln(x)/x c) 1/x d) ln²(x)/2
Answer: b) ln(x)/x
40. Let h(x) = ∫₀ˣ (1/(a²+t²)) dt, where a is a constant. What is h'(x)?
a) 1/(a²+x²) b) 2x/(a²+x²) c) a/(a²+x²) d) x/(a²+x²)
Answer: a) 1/(a²+x²)
41. If f(x) = ∫₀ˣ (1/√(1+t³)) dt, then f'(x) =
a) 1/√(1+x³) b) 3x²/√(1+x³) c) 1/(1+x³) d) 3/(1+x³)
Answer: a) 1/√(1+x³)
42. Given F(x) = ∫₀ˣ (t²e^t) dt, what is F'(x)?
a) x²e^x b) 2xe^x c) e^x d) x²e^x + 2xe^x
Answer: a) x²e^x
43. If g(x) = ∫₀ˣ (sin(t)/t²) dt, then g'(x) =
a) cos(x)/x² b) sin(x)/x² c) -sin(x)/x³ d) cos(x)/x
Answer: b) sin(x)/x²
44. Let h(x) = ∫₁ˣ (t ln²(t)) dt. What is h'(x)?
a) ln²(x) b) x ln²(x) c) 2x ln(x) d) 2 ln(x)
Answer: b) x ln²(x)
45. If f(x) = ∫₀ˣ (cos(t²)) dt, then f'(x) =
a) -2x sin(x²) b) cos(x²) c) -sin(x²) d) 2x cos(x²)
Answer: b) cos(x²)
46. Given F(x) = ∫₀ˣ (1/(1+e^t)) dt, what is F'(x)?
a) 1/(1+e^x) b) e^x/(1+e^x) c) 1/(1+e^(-x)) d) e^(-x)/(1+e^(-x))
Answer: a) 1/(1+e^x)
47. If g(x) = ∫₁ˣ (√(t²+1)) dt, then g'(x) =
a) √(x²+1) b) x/√(x²+1) c) 1/√(x²+1) d) x√(x²+1)
Answer: a) √(x²+1)
48. Let h(x) = ∫₀ˣ (t sin(t)) dt. What is h'(x)?
a) sin(x) b) x sin(x) c) cos(x) d) x cos(x)
Answer: b) x sin(x)
49. If f(x) = ∫₀ˣ (e^(-t²)) dt, then f'(x) =
a) -2xe^(-x²) b) e^(-x²) c) -e^(-x²) d) 2xe^(-x²)
Answer: b) e^(-x²)
. Given F(x) = ∫₀ˣ (t ln(t)) dt, what is F'(x)?
a) ln(x) b) x ln(x) c) x + ln(x) d) x ln(x) - x
Answer: b) x ln(x)
35. If g(x) = ∫₁ˣ (1/(1+t³)) dt, then g'(x) =
a) 1/(1+x³) b) 3x²/(1+x³) c) 1/(1+x) d) 3/(1+x³)
Answer: a) 1/(1+x³)
36. Let h(x) = ∫₀ˣ arccos(t) dt. What is h'(x)?
a) -1/√(1-x²) b) 1/√(1-x²) c) arccos(x) d) -arccos(x)
Answer: c) arccos(x)
37. If f(x) = ∫₀ˣ (t/(1+t²)) dt, then f'(x) =
a) 1/(1+x²) b) x/(1+x²) c) arctan(x) d) 2x/(1+x²)
Answer: b) x/(1+x²)
38. Given F(x) = ∫₀ˣ csc(t) dt, what is F'(x)?
a) sec(x) b) csc(x) c) cot(x) d) tan(x)
Answer: b) csc(x)
39. If g(x) = ∫₁ˣ (ln(t)/t) dt, then g'(x) =
a) ln(ln(x)) b) ln(x)/x c) 1/x d) ln²(x)/2
Answer: b) ln(x)/x
40. Let h(x) = ∫₀ˣ (1/(a²+t²)) dt, where a is a constant. What is h'(x)?
a) 1/(a²+x²) b) 2x/(a²+x²) c) a/(a²+x²) d) x/(a²+x²)
Answer: a) 1/(a²+x²)
41. If f(x) = ∫₀ˣ (1/√(1+t³)) dt, then f'(x) =
a) 1/√(1+x³) b) 3x²/√(1+x³) c) 1/(1+x³) d) 3/(1+x³)
Answer: a) 1/√(1+x³)
42. Given F(x) = ∫₀ˣ (t²e^t) dt, what is F'(x)?
a) x²e^x b) 2xe^x c) e^x d) x²e^x + 2xe^x
Answer: a) x²e^x
43. If g(x) = ∫₀ˣ (sin(t)/t²) dt, then g'(x) =
a) cos(x)/x² b) sin(x)/x² c) -sin(x)/x³ d) cos(x)/x
Answer: b) sin(x)/x²
44. Let h(x) = ∫₁ˣ (t ln²(t)) dt. What is h'(x)?
a) ln²(x) b) x ln²(x) c) 2x ln(x) d) 2 ln(x)
Answer: b) x ln²(x)
45. If f(x) = ∫₀ˣ (cos(t²)) dt, then f'(x) =
a) -2x sin(x²) b) cos(x²) c) -sin(x²) d) 2x cos(x²)
Answer: b) cos(x²)
46. Given F(x) = ∫₀ˣ (1/(1+e^t)) dt, what is F'(x)?
a) 1/(1+e^x) b) e^x/(1+e^x) c) 1/(1+e^(-x)) d) e^(-x)/(1+e^(-x))
Answer: a) 1/(1+e^x)
47. If g(x) = ∫₁ˣ (√(t²+1)) dt, then g'(x) =
a) √(x²+1) b) x/√(x²+1) c) 1/√(x²+1) d) x√(x²+1)
Answer: a) √(x²+1)
48. Let h(x) = ∫₀ˣ (t sin(t)) dt. What is h'(x)?
a) sin(x) b) x sin(x) c) cos(x) d) x cos(x)
Answer: b) x sin(x)
49. If f(x) = ∫₀ˣ (e^(-t²)) dt, then f'(x) =
a) -2xe^(-x²) b) e^(-x²) c) -e^(-x²) d) 2xe^(-x²)
Answer: b) e^(-x²)
. Given F(x) = ∫₀ˣ (t ln(t)) dt, what is F'(x)?
a) ln(x) b) x ln(x) c) x + ln(x) d) x ln(x) - x
Answer: b) x ln(x)
35. If g(x) = ∫₁ˣ (1/(1+t³)) dt, then g'(x) =
a) 1/(1+x³) b) 3x²/(1+x³) c) 1/(1+x) d) 3/(1+x³)
Answer: a) 1/(1+x³)
36. Let h(x) = ∫₀ˣ arccos(t) dt. What is h'(x)?
a) -1/√(1-x²) b) 1/√(1-x²) c) arccos(x) d) -arccos(x)
Answer: c) arccos(x)
37. If f(x) = ∫₀ˣ (t/(1+t²)) dt, then f'(x) =
a) 1/(1+x²) b) x/(1+x²) c) arctan(x) d) 2x/(1+x²)
Answer: b) x/(1+x²)
38. Given F(x) = ∫₀ˣ csc(t) dt, what is F'(x)?
a) sec(x) b) csc(x) c) cot(x) d) tan(x)
Answer: b) csc(x)
39. If g(x) = ∫₁ˣ (ln(t)/t) dt, then g'(x) =
a) ln(ln(x)) b) ln(x)/x c) 1/x d) ln²(x)/2
Answer: b) ln(x)/x
40. Let h(x) = ∫₀ˣ (1/(a²+t²)) dt, where a is a constant. What is h'(x)?
a) 1/(a²+x²) b) 2x/(a²+x²) c) a/(a²+x²) d) x/(a²+x²)
Answer: a) 1/(a²+x²)
41. If f(x) = ∫₀ˣ (1/√(1+t³)) dt, then f'(x) =
a) 1/√(1+x³) b) 3x²/√(1+x³) c) 1/(1+x³) d) 3/(1+x³)
Answer: a) 1/√(1+x³)
42. Given F(x) = ∫₀ˣ (t²e^t) dt, what is F'(x)?
a) x²e^x b) 2xe^x c) e^x d) x²e^x + 2xe^x
Answer: a) x²e^x
43. If g(x) = ∫₀ˣ (sin(t)/t²) dt, then g'(x) =
a) cos(x)/x² b) sin(x)/x² c) -sin(x)/x³ d) cos(x)/x
Answer: b) sin(x)/x²
44. Let h(x) = ∫₁ˣ (t ln²(t)) dt. What is h'(x)?
a) ln²(x) b) x ln²(x) c) 2x ln(x) d) 2 ln(x)
Answer: b) x ln²(x)
45. If f(x) = ∫₀ˣ (cos(t²)) dt, then f'(x) =
a) -2x sin(x²) b) cos(x²) c) -sin(x²) d) 2x cos(x²)
Answer: b) cos(x²)
46. Given F(x) = ∫₀ˣ (1/(1+e^t)) dt, what is F'(x)?
a) 1/(1+e^x) b) e^x/(1+e^x) c) 1/(1+e^(-x)) d) e^(-x)/(1+e^(-x))
Answer: a) 1/(1+e^x)
47. If g(x) = ∫₁ˣ (√(t²+1)) dt, then g'(x) =
a) √(x²+1) b) x/√(x²+1) c) 1/√(x²+1) d) x√(x²+1)
Answer: a) √(x²+1)
48. Let h(x) = ∫₀ˣ (t sin(t)) dt. What is h'(x)?
a) sin(x) b) x sin(x) c) cos(x) d) x cos(x)
Answer: b) x sin(x)
49. If f(x) = ∫₀ˣ (e^(-t²)) dt, then f'(x) =
a) -2xe^(-x²) b) e^(-x²) c) -e^(-x²) d) 2xe^(-x²)
Answer: b) e^(-x²)
. Given F(x) = ∫₀ˣ (t ln(t)) dt, what is F'(x)?
a) ln(x) b) x ln(x) c) x + ln(x) d) x ln(x) - x
Answer: b) x ln(x)
35. If g(x) = ∫₁ˣ (1/(1+t³)) dt, then g'(x) =
a) 1/(1+x³) b) 3x²/(1+x³) c) 1/(1+x) d) 3/(1+x³)
Answer: a) 1/(1+x³)
36. Let h(x) = ∫₀ˣ arccos(t) dt. What is h'(x)?
a) -1/√(1-x²) b) 1/√(1-x²) c) arccos(x) d) -arccos(x)
Answer: c) arccos(x)
37. If f(x) = ∫₀ˣ (t/(1+t²)) dt, then f'(x) =
a) 1/(1+x²) b) x/(1+x²) c) arctan(x) d) 2x/(1+x²)
Answer: b) x/(1+x²)
38. Given F(x) = ∫₀ˣ csc(t) dt, what is F'(x)?
a) sec(x) b) csc(x) c) cot(x) d) tan(x)
Answer: b) csc(x)
39. If g(x) = ∫₁ˣ (ln(t)/t) dt, then g'(x) =
a) ln(ln(x)) b) ln(x)/x c) 1/x d) ln²(x)/2
Answer: b) ln(x)/x
40. Let h(x) = ∫₀ˣ (1/(a²+t²)) dt, where a is a constant. What is h'(x)?
a) 1/(a²+x²) b) 2x/(a²+x²) c) a/(a²+x²) d) x/(a²+x²)
Answer: a) 1/(a²+x²)
41. If f(x) = ∫₀ˣ (1/√(1+t³)) dt, then f'(x) =
a) 1/√(1+x³) b) 3x²/√(1+x³) c) 1/(1+x³) d) 3/(1+x³)
Answer: a) 1/√(1+x³)
42. Given F(x) = ∫₀ˣ (t²e^t) dt, what is F'(x)?
a) x²e^x b) 2xe^x c) e^x d) x²e^x + 2xe^x
Answer: a) x²e^x
43. If g(x) = ∫₀ˣ (sin(t)/t²) dt, then g'(x) =
a) cos(x)/x² b) sin(x)/x² c) -sin(x)/x³ d) cos(x)/x
Answer: b) sin(x)/x²
44. Let h(x) = ∫₁ˣ (t ln²(t)) dt. What is h'(x)?
a) ln²(x) b) x ln²(x) c) 2x ln(x) d) 2 ln(x)
Answer: b) x ln²(x)
45. If f(x) = ∫₀ˣ (cos(t²)) dt, then f'(x) =
a) -2x sin(x²) b) cos(x²) c) -sin(x²) d) 2x cos(x²)
Answer: b) cos(x²)
46. Given F(x) = ∫₀ˣ (1/(1+e^t)) dt, what is F'(x)?
a) 1/(1+e^x) b) e^x/(1+e^x) c) 1/(1+e^(-x)) d) e^(-x)/(1+e^(-x))
Answer: a) 1/(1+e^x)
47. If g(x) = ∫₁ˣ (√(t²+1)) dt, then g'(x) =
a) √(x²+1) b) x/√(x²+1) c) 1/√(x²+1) d) x√(x²+1)
Answer: a) √(x²+1)
48. Let h(x) = ∫₀ˣ (t sin(t)) dt. What is h'(x)?
a) sin(x) b) x sin(x) c) cos(x) d) x cos(x)
Answer: b) x sin(x)
49. If f(x) = ∫₀ˣ (e^(-t²)) dt, then f'(x) =
a) -2xe^(-x²) b) e^(-x²) c) -e^(-x²) d) 2xe^(-x²)
Answer: b) e^(-x²)
. Given F(x) = ∫₀ˣ (t ln(t)) dt, what is F'(x)?
a) ln(x) b) x ln(x) c) x + ln(x) d) x ln(x) - x
Answer: b) x ln(x)
35. If g(x) = ∫₁ˣ (1/(1+t³)) dt, then g'(x) =
a) 1/(1+x³) b) 3x²/(1+x³) c) 1/(1+x) d) 3/(1+x³)
Answer: a) 1/(1+x³)
36. Let h(x) = ∫₀ˣ arccos(t) dt. What is h'(x)?
a) -1/√(1-x²) b) 1/√(1-x²) c) arccos(x) d) -arccos(x)
Answer: c) arccos(x)
37. If f(x) = ∫₀ˣ (t/(1+t²)) dt, then f'(x) =
a) 1/(1+x²) b) x/(1+x²) c) arctan(x) d) 2x/(1+x²)
Answer: b) x/(1+x²)
38. Given F(x) = ∫₀ˣ csc(t) dt, what is F'(x)?
a) sec(x) b) csc(x) c) cot(x) d) tan(x)
Answer: b) csc(x)
39. If g(x) = ∫₁ˣ (ln(t)/t) dt, then g'(x) =
a) ln(ln(x)) b) ln(x)/x c) 1/x d) ln²(x)/2
Answer: b) ln(x)/x
40. Let h(x) = ∫₀ˣ (1/(a²+t²)) dt, where a is a constant. What is h'(x)?
a) 1/(a²+x²) b) 2x/(a²+x²) c) a/(a²+x²) d) x/(a²+x²)
Answer: a) 1/(a²+x²)
41. If f(x) = ∫₀ˣ (1/√(1+t³)) dt, then f'(x) =
a) 1/√(1+x³) b) 3x²/√(1+x³) c) 1/(1+x³) d) 3/(1+x³)
Answer: a) 1/√(1+x³)
42. Given F(x) = ∫₀ˣ (t²e^t) dt, what is F'(x)?
a) x²e^x b) 2xe^x c) e^x d) x²e^x + 2xe^x
Answer: a) x²e^x
43. If g(x) = ∫₀ˣ (sin(t)/t²) dt, then g'(x) =
a) cos(x)/x² b) sin(x)/x² c) -sin(x)/x³ d) cos(x)/x
Answer: b) sin(x)/x²
44. Let h(x) = ∫₁ˣ (t ln²(t)) dt. What is h'(x)?
a) ln²(x) b) x ln²(x) c) 2x ln(x) d) 2 ln(x)
Answer: b) x ln²(x)
45. If f(x) = ∫₀ˣ (cos(t²)) dt, then f'(x) =
a) -2x sin(x²) b) cos(x²) c) -sin(x²) d) 2x cos(x²)
Answer: b) cos(x²)
46. Given F(x) = ∫₀ˣ (1/(1+e^t)) dt, what is F'(x)?
a) 1/(1+e^x) b) e^x/(1+e^x) c) 1/(1+e^(-x)) d) e^(-x)/(1+e^(-x))
Answer: a) 1/(1+e^x)
47. If g(x) = ∫₁ˣ (√(t²+1)) dt, then g'(x) =
a) √(x²+1) b) x/√(x²+1) c) 1/√(x²+1) d) x√(x²+1)
Answer: a) √(x²+1)
48. Let h(x) = ∫₀ˣ (t sin(t)) dt. What is h'(x)?
a) sin(x) b) x sin(x) c) cos(x) d) x cos(x)
Answer: b) x sin(x)
49. If f(x) = ∫₀ˣ (e^(-t²)) dt, then f'(x) =
a) -2xe^(-x²) b) e^(-x²) c) -e^(-x²) d) 2xe^(-x²)
Answer: b) e^(-x²)
. Given F(x) = ∫₀ˣ (t ln(t)) dt, what is F'(x)?
a) ln(x) b) x ln(x) c) x + ln(x) d) x ln(x) - x
Answer: b) x ln(x)
35. If g(x) = ∫₁ˣ (1/(1+t³)) dt, then g'(x) =
a) 1/(1+x³) b) 3x²/(1+x³) c) 1/(1+x) d) 3/(1+x³)
Answer: a) 1/(1+x³)
36. Let h(x) = ∫₀ˣ arccos(t) dt. What is h'(x)?
a) -1/√(1-x²) b) 1/√(1-x²) c) arccos(x) d) -arccos(x)
Answer: c) arccos(x)
37. If f(x) = ∫₀ˣ (t/(1+t²)) dt, then f'(x) =
a) 1/(1+x²) b) x/(1+x²) c) arctan(x) d) 2x/(1+x²)
Answer: b) x/(1+x²)
38. Given F(x) = ∫₀ˣ csc(t) dt, what is F'(x)?
a) sec(x) b) csc(x) c) cot(x) d) tan(x)
Answer: b) csc(x)
39. If g(x) = ∫₁ˣ (ln(t)/t) dt, then g'(x) =
a) ln(ln(x)) b) ln(x)/x c) 1/x d) ln²(x)/2
Answer: b) ln(x)/x
40. Let h(x) = ∫₀ˣ (1/(a²+t²)) dt, where a is a constant. What is h'(x)?
a) 1/(a²+x²) b) 2x/(a²+x²) c) a/(a²+x²) d) x/(a²+x²)
Answer: a) 1/(a²+x²)
41. If f(x) = ∫₀ˣ (1/√(1+t³)) dt, then f'(x) =
a) 1/√(1+x³) b) 3x²/√(1+x³) c) 1/(1+x³) d) 3/(1+x³)
Answer: a) 1/√(1+x³)
42. Given F(x) = ∫₀ˣ (t²e^t) dt, what is F'(x)?
a) x²e^x b) 2xe^x c) e^x d) x²e^x + 2xe^x
Answer: a) x²e^x
43. If g(x) = ∫₀ˣ (sin(t)/t²) dt, then g'(x) =
a) cos(x)/x² b) sin(x)/x² c) -sin(x)/x³ d) cos(x)/x
Answer: b) sin(x)/x²
44. Let h(x) = ∫₁ˣ (t ln²(t)) dt. What is h'(x)?
a) ln²(x) b) x ln²(x) c) 2x ln(x) d) 2 ln(x)
Answer: b) x ln²(x)
45. If f(x) = ∫₀ˣ (cos(t²)) dt, then f'(x) =
a) -2x sin(x²) b) cos(x²) c) -sin(x²) d) 2x cos(x²)
Answer: b) cos(x²)
46. Given F(x) = ∫₀ˣ (1/(1+e^t)) dt, what is F'(x)?
a) 1/(1+e^x) b) e^x/(1+e^x) c) 1/(1+e^(-x)) d) e^(-x)/(1+e^(-x))
Answer: a) 1/(1+e^x)
47. If g(x) = ∫₁ˣ (√(t²+1)) dt, then g'(x) =
a) √(x²+1) b) x/√(x²+1) c) 1/√(x²+1) d) x√(x²+1)
Answer: a) √(x²+1)
48. Let h(x) = ∫₀ˣ (t sin(t)) dt. What is h'(x)?
a) sin(x) b) x sin(x) c) cos(x) d) x cos(x)
Answer: b) x sin(x)
49. If f(x) = ∫₀ˣ (e^(-t²)) dt, then f'(x) =
a) -2xe^(-x²) b) e^(-x²) c) -e^(-x²) d) 2xe^(-x²)
Answer: b) e^(-x²)
. Given F(x) = ∫₀ˣ (t ln(t)) dt, what is F'(x)?
a) ln(x) b) x ln(x) c) x + ln(x) d) x ln(x) - x
Answer: b) x ln(x)
35. If g(x) = ∫₁ˣ (1/(1+t³)) dt, then g'(x) =
a) 1/(1+x³) b) 3x²/(1+x³) c) 1/(1+x) d) 3/(1+x³)
Answer: a) 1/(1+x³)
36. Let h(x) = ∫₀ˣ arccos(t) dt. What is h'(x)?
a) -1/√(1-x²) b) 1/√(1-x²) c) arccos(x) d) -arccos(x)
Answer: c) arccos(x)
37. If f(x) = ∫₀ˣ (t/(1+t²)) dt, then f'(x) =
a) 1/(1+x²) b) x/(1+x²) c) arctan(x) d) 2x/(1+x²)
Answer: b) x/(1+x²)
38. Given F(x) = ∫₀ˣ csc(t) dt, what is F'(x)?
a) sec(x) b) csc(x) c) cot(x) d) tan(x)
Answer: b) csc(x)
39. If g(x) = ∫₁ˣ (ln(t)/t) dt, then g'(x) =
a) ln(ln(x)) b) ln(x)/x c) 1/x d) ln²(x)/2
Answer: b) ln(x)/x
40. Let h(x) = ∫₀ˣ (1/(a²+t²)) dt, where a is a constant. What is h'(x)?
a) 1/(a²+x²) b) 2x/(a²+x²) c) a/(a²+x²) d) x/(a²+x²)
Answer: a) 1/(a²+x²)
41. If f(x) = ∫₀ˣ (1/√(1+t³)) dt, then f'(x) =
a) 1/√(1+x³) b) 3x²/√(1+x³) c) 1/(1+x³) d) 3/(1+x³)
Answer: a) 1/√(1+x³)
42. Given F(x) = ∫₀ˣ (t²e^t) dt, what is F'(x)?
a) x²e^x b) 2xe^x c) e^x d) x²e^x + 2xe^x
Answer: a) x²e^x
43. If g(x) = ∫₀ˣ (sin(t)/t²) dt, then g'(x) =
a) cos(x)/x² b) sin(x)/x² c) -sin(x)/x³ d) cos(x)/x
Answer: b) sin(x)/x²
44. Let h(x) = ∫₁ˣ (t ln²(t)) dt. What is h'(x)?
a) ln²(x) b) x ln²(x) c) 2x ln(x) d) 2 ln(x)
Answer: b) x ln²(x)
45. If f(x) = ∫₀ˣ (cos(t²)) dt, then f'(x) =
a) -2x sin(x²) b) cos(x²) c) -sin(x²) d) 2x cos(x²)
Answer: b) cos(x²)
46. Given F(x) = ∫₀ˣ (1/(1+e^t)) dt, what is F'(x)?
a) 1/(1+e^x) b) e^x/(1+e^x) c) 1/(1+e^(-x)) d) e^(-x)/(1+e^(-x))
Answer: a) 1/(1+e^x)
47. If g(x) = ∫₁ˣ (√(t²+1)) dt, then g'(x) =
a) √(x²+1) b) x/√(x²+1) c) 1/√(x²+1) d) x√(x²+1)
Answer: a) √(x²+1)
48. Let h(x) = ∫₀ˣ (t sin(t)) dt. What is h'(x)?
a) sin(x) b) x sin(x) c) cos(x) d) x cos(x)
Answer: b) x sin(x)
49. If f(x) = ∫₀ˣ (e^(-t²)) dt, then f'(x) =
a) -2xe^(-x²) b) e^(-x²) c) -e^(-x²) d) 2xe^(-x²)
Answer: b) e^(-x²)
. Given F(x) = ∫₀ˣ (t ln(t)) dt, what is F'(x)?
a) ln(x) b) x ln(x) c) x + ln(x) d) x ln(x) - x
Answer: b) x ln(x)
35. If g(x) = ∫₁ˣ (1/(1+t³)) dt, then g'(x) =
a) 1/(1+x³) b) 3x²/(1+x³) c) 1/(1+x) d) 3/(1+x³)
Answer: a) 1/(1+x³)
36. Let h(x) = ∫₀ˣ arccos(t) dt. What is h'(x)?
a) -1/√(1-x²) b) 1/√(1-x²) c) arccos(x) d) -arccos(x)
Answer: c) arccos(x)
37. If f(x) = ∫₀ˣ (t/(1+t²)) dt, then f'(x) =
a) 1/(1+x²) b) x/(1+x²) c) arctan(x) d) 2x/(1+x²)
Answer: b) x/(1+x²)
38. Given F(x) = ∫₀ˣ csc(t) dt, what is F'(x)?
a) sec(x) b) csc(x) c) cot(x) d) tan(x)
Answer: b) csc(x)
39. If g(x) = ∫₁ˣ (ln(t)/t) dt, then g'(x) =
a) ln(ln(x)) b) ln(x)/x c) 1/x d) ln²(x)/2
Answer: b) ln(x)/x
40. Let h(x) = ∫₀ˣ (1/(a²+t²)) dt, where a is a constant. What is h'(x)?
a) 1/(a²+x²) b) 2x/(a²+x²) c) a/(a²+x²) d) x/(a²+x²)
Answer: a) 1/(a²+x²)
41. If f(x) = ∫₀ˣ (1/√(1+t³)) dt, then f'(x) =
a) 1/√(1+x³) b) 3x²/√(1+x³) c) 1/(1+x³) d) 3/(1+x³)
Answer: a) 1/√(1+x³)
42. Given F(x) = ∫₀ˣ (t²e^t) dt, what is F'(x)?
a) x²e^x b) 2xe^x c) e^x d) x²e^x + 2xe^x
Answer: a) x²e^x
43. If g(x) = ∫₀ˣ (sin(t)/t²) dt, then g'(x) =
a) cos(x)/x² b) sin(x)/x² c) -sin(x)/x³ d) cos(x)/x
Answer: b) sin(x)/x²
44. Let h(x) = ∫₁ˣ (t ln²(t)) dt. What is h'(x)?
a) ln²(x) b) x ln²(x) c) 2x ln(x) d) 2 ln(x)
Answer: b) x ln²(x)
45. If f(x) = ∫₀ˣ (cos(t²)) dt, then f'(x) =
a) -2x sin(x²) b) cos(x²) c) -sin(x²) d) 2x cos(x²)
Answer: b) cos(x²)
46. Given F(x) = ∫₀ˣ (1/(1+e^t)) dt, what is F'(x)?
a) 1/(1+e^x) b) e^x/(1+e^x) c) 1/(1+e^(-x)) d) e^(-x)/(1+e^(-x))
Answer: a) 1/(1+e^x)
47. If g(x) = ∫₁ˣ (√(t²+1)) dt, then g'(x) =
a) √(x²+1) b) x/√(x²+1) c) 1/√(x²+1) d) x√(x²+1)
Answer: a) √(x²+1)
48. Let h(x) = ∫₀ˣ (t sin(t)) dt. What is h'(x)?
a) sin(x) b) x sin(x) c) cos(x) d) x cos(x)
Answer: b) x sin(x)
49. If f(x) = ∫₀ˣ (e^(-t²)) dt, then f'(x) =
a) -2xe^(-x²) b) e^(-x²) c) -e^(-x²) d) 2xe^(-x²)
Answer: b) e^(-x²)
. Given F(x) = ∫₀ˣ (t ln(t)) dt, what is F'(x)?
a) ln(x) b) x ln(x) c) x + ln(x) d) x ln(x) - x
Answer: b) x ln(x)
35. If g(x) = ∫₁ˣ (1/(1+t³)) dt, then g'(x) =
a) 1/(1+x³) b) 3x²/(1+x³) c) 1/(1+x) d) 3/(1+x³)
Answer: a) 1/(1+x³)
36. Let h(x) = ∫₀ˣ arccos(t) dt. What is h'(x)?
a) -1/√(1-x²) b) 1/√(1-x²) c) arccos(x) d) -arccos(x)
Answer: c) arccos(x)
37. If f(x) = ∫₀ˣ (t/(1+t²)) dt, then f'(x) =
a) 1/(1+x²) b) x/(1+x²) c) arctan(x) d) 2x/(1+x²)
Answer: b) x/(1+x²)
38. Given F(x) = ∫₀ˣ csc(t) dt, what is F'(x)?
a) sec(x) b) csc(x) c) cot(x) d) tan(x)
Answer: b) csc(x)
39. If g(x) = ∫₁ˣ (ln(t)/t) dt, then g'(x) =
a) ln(ln(x)) b) ln(x)/x c) 1/x d) ln²(x)/2
Answer: b) ln(x)/x
40. Let h(x) = ∫₀ˣ (1/(a²+t²)) dt, where a is a constant. What is h'(x)?
a) 1/(a²+x²) b) 2x/(a²+x²) c) a/(a²+x²) d) x/(a²+x²)
Answer: a) 1/(a²+x²)
41. If f(x) = ∫₀ˣ (1/√(1+t³)) dt, then f'(x) =
a) 1/√(1+x³) b) 3x²/√(1+x³) c) 1/(1+x³) d) 3/(1+x³)
Answer: a) 1/√(1+x³)
42. Given F(x) = ∫₀ˣ (t²e^t) dt, what is F'(x)?
a) x²e^x b) 2xe^x c) e^x d) x²e^x + 2xe^x
Answer: a) x²e^x
43. If g(x) = ∫₀ˣ (sin(t)/t²) dt, then g'(x) =
a) cos(x)/x² b) sin(x)/x² c) -sin(x)/x³ d) cos(x)/x
Answer: b) sin(x)/x²
44. Let h(x) = ∫₁ˣ (t ln²(t)) dt. What is h'(x)?
a) ln²(x) b) x ln²(x) c) 2x ln(x) d) 2 ln(x)
Answer: b) x ln²(x)
45. If f(x) = ∫₀ˣ (cos(t²)) dt, then f'(x) =
a) -2x sin(x²) b) cos(x²) c) -sin(x²) d) 2x cos(x²)
Answer: b) cos(x²)
46. Given F(x) = ∫₀ˣ (1/(1+e^t)) dt, what is F'(x)?
a) 1/(1+e^x) b) e^x/(1+e^x) c) 1/(1+e^(-x)) d) e^(-x)/(1+e^(-x))
Answer: a) 1/(1+e^x)
47. If g(x) = ∫₁ˣ (√(t²+1)) dt, then g'(x) =
a) √(x²+1) b) x/√(x²+1) c) 1/√(x²+1) d) x√(x²+1)
Answer: a) √(x²+1)
48. Let h(x) = ∫₀ˣ (t sin(t)) dt. What is h'(x)?
a) sin(x) b) x sin(x) c) cos(x) d) x cos(x)
Answer: b) x sin(x)
49. If f(x) = ∫₀ˣ (e^(-t²)) dt, then f'(x) =
a) -2xe^(-x²) b) e^(-x²) c) -e^(-x²) d) 2xe^(-x²)
Answer: b) e^(-x²)
. Given F(x) = ∫₀ˣ (t ln(t)) dt, what is F'(x)?
a) ln(x) b) x ln(x) c) x + ln(x) d) x ln(x) - x
Answer: b) x ln(x)
35. If g(x) = ∫₁ˣ (1/(1+t³)) dt, then g'(x) =
a) 1/(1+x³) b) 3x²/(1+x³) c) 1/(1+x) d) 3/(1+x³)
Answer: a) 1/(1+x³)
36. Let h(x) = ∫₀ˣ arccos(t) dt. What is h'(x)?
a) -1/√(1-x²) b) 1/√(1-x²) c) arccos(x) d) -arccos(x)
Answer: c) arccos(x)
37. If f(x) = ∫₀ˣ (t/(1+t²)) dt, then f'(x) =
a) 1/(1+x²) b) x/(1+x²) c) arctan(x) d) 2x/(1+x²)
Answer: b) x/(1+x²)
38. Given F(x) = ∫₀ˣ csc(t) dt, what is F'(x)?
a) sec(x) b) csc(x) c) cot(x) d) tan(x)
Answer: b) csc(x)
39. If g(x) = ∫₁ˣ (ln(t)/t) dt, then g'(x) =
a) ln(ln(x)) b) ln(x)/x c) 1/x d) ln²(x)/2
Answer: b) ln(x)/x
40. Let h(x) = ∫₀ˣ (1/(a²+t²)) dt, where a is a constant. What is h'(x)?
a) 1/(a²+x²) b) 2x/(a²+x²) c) a/(a²+x²) d) x/(a²+x²)
Answer: a) 1/(a²+x²)
41. If f(x) = ∫₀ˣ (1/√(1+t³)) dt, then f'(x) =
a) 1/√(1+x³) b) 3x²/√(1+x³) c) 1/(1+x³) d) 3/(1+x³)
Answer: a) 1/√(1+x³)
42. Given F(x) = ∫₀ˣ (t²e^t) dt, what is F'(x)?
a) x²e^x b) 2xe^x c) e^x d) x²e^x + 2xe^x
Answer: a) x²e^x
43. If g(x) = ∫₀ˣ (sin(t)/t²) dt, then g'(x) =
a) cos(x)/x² b) sin(x)/x² c) -sin(x)/x³ d) cos(x)/x
Answer: b) sin(x)/x²
44. Let h(x) = ∫₁ˣ (t ln²(t)) dt. What is h'(x)?
a) ln²(x) b) x ln²(x) c) 2x ln(x) d) 2 ln(x)
Answer: b) x ln²(x)
45. If f(x) = ∫₀ˣ (cos(t²)) dt, then f'(x) =
a) -2x sin(x²) b) cos(x²) c) -sin(x²) d) 2x cos(x²)
Answer: b) cos(x²)
46. Given F(x) = ∫₀ˣ (1/(1+e^t)) dt, what is F'(x)?
a) 1/(1+e^x) b) e^x/(1+e^x) c) 1/(1+e^(-x)) d) e^(-x)/(1+e^(-x))
Answer: a) 1/(1+e^x)
47. If g(x) = ∫₁ˣ (√(t²+1)) dt, then g'(x) =
a) √(x²+1) b) x/√(x²+1) c) 1/√(x²+1) d) x√(x²+1)
Answer: a) √(x²+1)
48. Let h(x) = ∫₀ˣ (t sin(t)) dt. What is h'(x)?
a) sin(x) b) x sin(x) c) cos(x) d) x cos(x)
Answer: b) x sin(x)
49. If f(x) = ∫₀ˣ (e^(-t²)) dt, then f'(x) =
a) -2xe^(-x²) b) e^(-x²) c) -e^(-x²) d) 2xe^(-x²)
Answer: b) e^(-x²)
. Given F(x) = ∫₀ˣ (t ln(t)) dt, what is F'(x)?
a) ln(x) b) x ln(x) c) x + ln(x) d) x ln(x) - x
Answer: b) x ln(x)
35. If g(x) = ∫₁ˣ (1/(1+t³)) dt, then g'(x) =
a) 1/(1+x³) b) 3x²/(1+x³) c) 1/(1+x) d) 3/(1+x³)
Answer: a) 1/(1+x³)
36. Let h(x) = ∫₀ˣ arccos(t) dt. What is h'(x)?
a) -1/√(1-x²) b) 1/√(1-x²) c) arccos(x) d) -arccos(x)
Answer: c) arccos(x)
37. If f(x) = ∫₀ˣ (t/(1+t²)) dt, then f'(x) =
a) 1/(1+x²) b) x/(1+x²) c) arctan(x) d) 2x/(1+x²)
Answer: b) x/(1+x²)
38. Given F(x) = ∫₀ˣ csc(t) dt, what is F'(x)?
a) sec(x) b) csc(x) c) cot(x) d) tan(x)
Answer: b) csc(x)
39. If g(x) = ∫₁ˣ (ln(t)/t) dt, then g'(x) =
a) ln(ln(x)) b) ln(x)/x c) 1/x d) ln²(x)/2
Answer: b) ln(x)/x
40. Let h(x) = ∫₀ˣ (1/(a²+t²)) dt, where a is a constant. What is h'(x)?
a) 1/(a²+x²) b) 2x/(a²+x²) c) a/(a²+x²) d) x/(a²+x²)
Answer: a) 1/(a²+x²)
41. If f(x) = ∫₀ˣ (1/√(1+t³)) dt, then f'(x) =
a) 1/√(1+x³) b) 3x²/√(1+x³) c) 1/(1+x³) d) 3/(1+x³)
Answer: a) 1/√(1+x³)
42. Given F(x) = ∫₀ˣ (t²e^t) dt, what is F'(x)?
a) x²e^x b) 2xe^x c) e^x d) x²e^x + 2xe^x
Answer: a) x²e^x
43. If g(x) = ∫₀ˣ (sin(t)/t²) dt, then g'(x) =
a) cos(x)/x² b) sin(x)/x² c) -sin(x)/x³ d) cos(x)/x
Answer: b) sin(x)/x²
44. Let h(x) = ∫₁ˣ (t ln²(t)) dt. What is h'(x)?
a) ln²(x) b) x ln²(x) c) 2x ln(x) d) 2 ln(x)
Answer: b) x ln²(x)
45. If f(x) = ∫₀ˣ (cos(t²)) dt, then f'(x) =
a) -2x sin(x²) b) cos(x²) c) -sin(x²) d) 2x cos(x²)
Answer: b) cos(x²)
46. Given F(x) = ∫₀ˣ (1/(1+e^t)) dt, what is F'(x)?
a) 1/(1+e^x) b) e^x/(1+e^x) c) 1/(1+e^(-x)) d) e^(-x)/(1+e^(-x))
Answer: a) 1/(1+e^x)
47. If g(x) = ∫₁ˣ (√(t²+1)) dt, then g'(x) =
a) √(x²+1) b) x/√(x²+1) c) 1/√(x²+1) d) x√(x²+1)
Answer: a) √(x²+1)
48. Let h(x) = ∫₀ˣ (t sin(t)) dt. What is h'(x)?
a) sin(x) b) x sin(x) c) cos(x) d) x cos(x)
Answer: b) x sin(x)
49. If f(x) = ∫₀ˣ (e^(-t²)) dt, then f'(x) =
a) -2xe^(-x²) b) e^(-x²) c) -e^(-x²) d) 2xe^(-x²)
Answer: b) e^(-x²)
. Given F(x) = ∫₀ˣ (t ln(t)) dt, what is F'(x)?
a) ln(x) b) x ln(x) c) x + ln(x) d) x ln(x) - x
Answer: b) x ln(x)
35. If g(x) = ∫₁ˣ (1/(1+t³)) dt, then g'(x) =
a) 1/(1+x³) b) 3x²/(1+x³) c) 1/(1+x) d) 3/(1+x³)
Answer: a) 1/(1+x³)
36. Let h(x) = ∫₀ˣ arccos(t) dt. What is h'(x)?
a) -1/√(1-x²) b) 1/√(1-x²) c) arccos(x) d) -arccos(x)
Answer: c) arccos(x)
37. If f(x) = ∫₀ˣ (t/(1+t²)) dt, then f'(x) =
a) 1/(1+x²) b) x/(1+x²) c) arctan(x) d) 2x/(1+x²)
Answer: b) x/(1+x²)
38. Given F(x) = ∫₀ˣ csc(t) dt, what is F'(x)?
a) sec(x) b) csc(x) c) cot(x) d) tan(x)
Answer: b) csc(x)
39. If g(x) = ∫₁ˣ (ln(t)/t) dt, then g'(x) =
a) ln(ln(x)) b) ln(x)/x c) 1/x d) ln²(x)/2
Answer: b) ln(x)/x
40. Let h(x) = ∫₀ˣ (1/(a²+t²)) dt, where a is a constant. What is h'(x)?
a) 1/(a²+x²) b) 2x/(a²+x²) c) a/(a²+x²) d) x/(a²+x²)
Answer: a) 1/(a²+x²)
41. If f(x) = ∫₀ˣ (1/√(1+t³)) dt, then f'(x) =
a) 1/√(1+x³) b) 3x²/√(1+x³) c) 1/(1+x³) d) 3/(1+x³)
Answer: a) 1/√(1+x³)
42. Given F(x) = ∫₀ˣ (t²e^t) dt, what is F'(x)?
a) x²e^x b) 2xe^x c) e^x d) x²e^x + 2xe^x
Answer: a) x²e^x
43. If g(x) = ∫₀ˣ (sin(t)/t²) dt, then g'(x) =
a) cos(x)/x² b) sin(x)/x² c) -sin(x)/x³ d) cos(x)/x
Answer: b) sin(x)/x²
44. Let h(x) = ∫₁ˣ (t ln²(t)) dt. What is h'(x)?
a) ln²(x) b) x ln²(x) c) 2x ln(x) d) 2 ln(x)
Answer: b) x ln²(x)
45. If f(x) = ∫₀ˣ (cos(t²)) dt, then f'(x) =
a) -2x sin(x²) b) cos(x²) c) -sin(x²) d) 2x cos(x²)
Answer: b) cos(x²)
46. Given F(x) = ∫₀ˣ (1/(1+e^t)) dt, what is F'(x)?
a) 1/(1+e^x) b) e^x/(1+e^x) c) 1/(1+e^(-x)) d) e^(-x)/(1+e^(-x))
Answer: a) 1/(1+e^x)
47. If g(x) = ∫₁ˣ (√(t²+1)) dt, then g'(x) =
a) √(x²+1) b) x/√(x²+1) c) 1/√(x²+1) d) x√(x²+1)
Answer: a) √(x²+1)
48. Let h(x) = ∫₀ˣ (t sin(t)) dt. What is h'(x)?
a) sin(x) b) x sin(x) c) cos(x) d) x cos(x)
Answer: b) x sin(x)
49. If f(x) = ∫₀ˣ (e^(-t²)) dt, then f'(x) =
a) -2xe^(-x²) b) e^(-x²) c) -e^(-x²) d) 2xe^(-x²)
Answer: b) e^(-x²)
. Given F(x) = ∫₀ˣ (t ln(t)) dt, what is F'(x)?
a) ln(x) b) x ln(x) c) x + ln(x) d) x ln(x) - x
Answer: b) x ln(x)
35. If g(x) = ∫₁ˣ (1/(1+t³)) dt, then g'(x) =
a) 1/(1+x³) b) 3x²/(1+x³) c) 1/(1+x) d) 3/(1+x³)
Answer: a) 1/(1+x³)
36. Let h(x) = ∫₀ˣ arccos(t) dt. What is h'(x)?
a) -1/√(1-x²) b) 1/√(1-x²) c) arccos(x) d) -arccos(x)
Answer: c) arccos(x)
37. If f(x) = ∫₀ˣ (t/(1+t²)) dt, then f'(x) =
a) 1/(1+x²) b) x/(1+x²) c) arctan(x) d) 2x/(1+x²)
Answer: b) x/(1+x²)
38. Given F(x) = ∫₀ˣ csc(t) dt, what is F'(x)?
a) sec(x) b) csc(x) c) cot(x) d) tan(x)
Answer: b) csc(x)
39. If g(x) = ∫₁ˣ (ln(t)/t) dt, then g'(x) =
a) ln(ln(x)) b) ln(x)/x c) 1/x d) ln²(x)/2
Answer: b) ln(x)/x
40. Let h(x) = ∫₀ˣ (1/(a²+t²)) dt, where a is a constant. What is h'(x)?
a) 1/(a²+x²) b) 2x/(a²+x²) c) a/(a²+x²) d) x/(a²+x²)
Answer: a) 1/(a²+x²)
41. If f(x) = ∫₀ˣ (1/√(1+t³)) dt, then f'(x) =
a) 1/√(1+x³) b) 3x²/√(1+x³) c) 1/(1+x³) d) 3/(1+x³)
Answer: a) 1/√(1+x³)
42. Given F(x) = ∫₀ˣ (t²e^t) dt, what is F'(x)?
a) x²e^x b) 2xe^x c) e^x d) x²e^x + 2xe^x
Answer: a) x²e^x
43. If g(x) = ∫₀ˣ (sin(t)/t²) dt, then g'(x) =
a) cos(x)/x² b) sin(x)/x² c) -sin(x)/x³ d) cos(x)/x
Answer: b) sin(x)/x²
44. Let h(x) = ∫₁ˣ (t ln²(t)) dt. What is h'(x)?
a) ln²(x) b) x ln²(x) c) 2x ln(x) d) 2 ln(x)
Answer: b) x ln²(x)
45. If f(x) = ∫₀ˣ (cos(t²)) dt, then f'(x) =
a) -2x sin(x²) b) cos(x²) c) -sin(x²) d) 2x cos(x²)
Answer: b) cos(x²)
46. Given F(x) = ∫₀ˣ (1/(1+e^t)) dt, what is F'(x)?
a) 1/(1+e^x) b) e^x/(1+e^x) c) 1/(1+e^(-x)) d) e^(-x)/(1+e^(-x))
Answer: a) 1/(1+e^x)
47. If g(x) = ∫₁ˣ (√(t²+1)) dt, then g'(x) =
a) √(x²+1) b) x/√(x²+1) c) 1/√(x²+1) d) x√(x²+1)
Answer: a) √(x²+1)
48. Let h(x) = ∫₀ˣ (t sin(t)) dt. What is h'(x)?
a) sin(x) b) x sin(x) c) cos(x) d) x cos(x)
Answer: b) x sin(x)
49. If f(x) = ∫₀ˣ (e^(-t²)) dt, then f'(x) =
a) -2xe^(-x²) b) e^(-x²) c) -e^(-x²) d) 2xe^(-x²)
Answer: b) e^(-x²)
. Given F(x) = ∫₀ˣ (t ln(t)) dt, what is F'(x)?
a) ln(x) b) x ln(x) c) x + ln(x) d) x ln(x) - x
Answer: b) x ln(x)
35. If g(x) = ∫₁ˣ (1/(1+t³)) dt, then g'(x) =
a) 1/(1+x³) b) 3x²/(1+x³) c) 1/(1+x) d) 3/(1+x³)
Answer: a) 1/(1+x³)
36. Let h(x) = ∫₀ˣ arccos(t) dt. What is h'(x)?
a) -1/√(1-x²) b) 1/√(1-x²) c) arccos(x) d) -arccos(x)
Answer: c) arccos(x)
37. If f(x) = ∫₀ˣ (t/(1+t²)) dt, then f'(x) =
a) 1/(1+x²) b) x/(1+x²) c) arctan(x) d) 2x/(1+x²)
Answer: b) x/(1+x²)
38. Given F(x) = ∫₀ˣ csc(t) dt, what is F'(x)?
a) sec(x) b) csc(x) c) cot(x) d) tan(x)
Answer: b) csc(x)
39. If g(x) = ∫₁ˣ (ln(t)/t) dt, then g'(x) =
a) ln(ln(x)) b) ln(x)/x c) 1/x d) ln²(x)/2
Answer: b) ln(x)/x
40. Let h(x) = ∫₀ˣ (1/(a²+t²)) dt, where a is a constant. What is h'(x)?
a) 1/(a²+x²) b) 2x/(a²+x²) c) a/(a²+x²) d) x/(a²+x²)
Answer: a) 1/(a²+x²)
41. If f(x) = ∫₀ˣ (1/√(1+t³)) dt, then f'(x) =
a) 1/√(1+x³) b) 3x²/√(1+x³) c) 1/(1+x³) d) 3/(1+x³)
Answer: a) 1/√(1+x³)
42. Given F(x) = ∫₀ˣ (t²e^t) dt, what is F'(x)?
a) x²e^x b) 2xe^x c) e^x d) x²e^x + 2xe^x
Answer: a) x²e^x
43. If g(x) = ∫₀ˣ (sin(t)/t²) dt, then g'(x) =
a) cos(x)/x² b) sin(x)/x² c) -sin(x)/x³ d) cos(x)/x
Answer: b) sin(x)/x²
44. Let h(x) = ∫₁ˣ (t ln²(t)) dt. What is h'(x)?
a) ln²(x) b) x ln²(x) c) 2x ln(x) d) 2 ln(x)
Answer: b) x ln²(x)
45. If f(x) = ∫₀ˣ (cos(t²)) dt, then f'(x) =
a) -2x sin(x²) b) cos(x²) c) -sin(x²) d) 2x cos(x²)
Answer: b) cos(x²)
46. Given F(x) = ∫₀ˣ (1/(1+e^t)) dt, what is F'(x)?
a) 1/(1+e^x) b) e^x/(1+e^x) c) 1/(1+e^(-x)) d) e^(-x)/(1+e^(-x))
Answer: a) 1/(1+e^x)
47. If g(x) = ∫₁ˣ (√(t²+1)) dt, then g'(x) =
a) √(x²+1) b) x/√(x²+1) c) 1/√(x²+1) d) x√(x²+1)
Answer: a) √(x²+1)
48. Let h(x) = ∫₀ˣ (t sin(t)) dt. What is h'(x)?
a) sin(x) b) x sin(x) c) cos(x) d) x cos(x)
Answer: b) x sin(x)
49. If f(x) = ∫₀ˣ (e^(-t²)) dt, then f'(x) =
a) -2xe^(-x²) b) e^(-x²) c) -e^(-x²) d) 2xe^(-x²)
Answer: b) e^(-x²)
. Given F(x) = ∫₀ˣ (t ln(t)) dt, what is F'(x)?
a) ln(x) b) x ln(x) c) x + ln(x) d) x ln(x) - x
Answer: b) x ln(x)
35. If g(x) = ∫₁ˣ (1/(1+t³)) dt, then g'(x) =
a) 1/(1+x³) b) 3x²/(1+x³) c) 1/(1+x) d) 3/(1+x³)
Answer: a) 1/(1+x³)
36. Let h(x) = ∫₀ˣ arccos(t) dt. What is h'(x)?
a) -1/√(1-x²) b) 1/√(1-x²) c) arccos(x) d) -arccos(x)
Answer: c) arccos(x)
37. If f(x) = ∫₀ˣ (t/(1+t²)) dt, then f'(x) =
a) 1/(1+x²) b) x/(1+x²) c) arctan(x) d) 2x/(1+x²)
Answer: b) x/(1+x²)
38. Given F(x) = ∫₀ˣ csc(t) dt, what is F'(x)?
a) sec(x) b) csc(x) c) cot(x) d) tan(x)
Answer: b) csc(x)
39. If g(x) = ∫₁ˣ (ln(t)/t) dt, then g'(x) =
a) ln(ln(x)) b) ln(x)/x c) 1/x d) ln²(x)/2
Answer: b) ln(x)/x
40. Let h(x) = ∫₀ˣ (1/(a²+t²)) dt, where a is a constant. What is h'(x)?
a) 1/(a²+x²) b) 2x/(a²+x²) c) a/(a²+x²) d) x/(a²+x²)
Answer: a) 1/(a²+x²)
41. If f(x) = ∫₀ˣ (1/√(1+t³)) dt, then f'(x) =
a) 1/√(1+x³) b) 3x²/√(1+x³) c) 1/(1+x³) d) 3/(1+x³)
Answer: a) 1/√(1+x³)
42. Given F(x) = ∫₀ˣ (t²e^t) dt, what is F'(x)?
a) x²e^x b) 2xe^x c) e^x d) x²e^x + 2xe^x
Answer: a) x²e^x
43. If g(x) = ∫₀ˣ (sin(t)/t²) dt, then g'(x) =
a) cos(x)/x² b) sin(x)/x² c) -sin(x)/x³ d) cos(x)/x
Answer: b) sin(x)/x²
44. Let h(x) = ∫₁ˣ (t ln²(t)) dt. What is h'(x)?
a) ln²(x) b) x ln²(x) c) 2x ln(x) d) 2 ln(x)
Answer: b) x ln²(x)
45. If f(x) = ∫₀ˣ (cos(t²)) dt, then f'(x) =
a) -2x sin(x²) b) cos(x²) c) -sin(x²) d) 2x cos(x²)
Answer: b) cos(x²)
46. Given F(x) = ∫₀ˣ (1/(1+e^t)) dt, what is F'(x)?
a) 1/(1+e^x) b) e^x/(1+e^x) c) 1/(1+e^(-x)) d) e^(-x)/(1+e^(-x))
Answer: a) 1/(1+e^x)
47. If g(x) = ∫₁ˣ (√(t²+1)) dt, then g'(x) =
a) √(x²+1) b) x/√(x²+1) c) 1/√(x²+1) d) x√(x²+1)
Answer: a) √(x²+1)
48. Let h(x) = ∫₀ˣ (t sin(t)) dt. What is h'(x)?
a) sin(x) b) x sin(x) c) cos(x) d) x cos(x)
Answer: b) x sin(x)
49. If f(x) = ∫₀ˣ (e^(-t²)) dt, then f'(x) =
a) -2xe^(-x²) b) e^(-x²) c) -e^(-x²) d) 2xe^(-x²)
Answer: b) e^(-x²)
. Given F(x) = ∫₀ˣ (t ln(t)) dt, what is F'(x)?
a) ln(x) b) x ln(x) c) x + ln(x) d) x ln(x) - x
Answer: b) x ln(x)
35. If g(x) = ∫₁ˣ (1/(1+t³)) dt, then g'(x) =
a) 1/(1+x³) b) 3x²/(1+x³) c) 1/(1+x) d) 3/(1+x³)
Answer: a) 1/(1+x³)
36. Let h(x) = ∫₀ˣ arccos(t) dt. What is h'(x)?
a) -1/√(1-x²) b) 1/√(1-x²) c) arccos(x) d) -arccos(x)
Answer: c) arccos(x)
37. If f(x) = ∫₀ˣ (t/(1+t²)) dt, then f'(x) =
a) 1/(1+x²) b) x/(1+x²) c) arctan(x) d) 2x/(1+x²)
Answer: b) x/(1+x²)
38. Given F(x) = ∫₀ˣ csc(t) dt, what is F'(x)?
a) sec(x) b) csc(x) c) cot(x) d) tan(x)
Answer: b) csc(x)
39. If g(x) = ∫₁ˣ (ln(t)/t) dt, then g'(x) =
a) ln(ln(x)) b) ln(x)/x c) 1/x d) ln²(x)/2
Answer: b) ln(x)/x
40. Let h(x) = ∫₀ˣ (1/(a²+t²)) dt, where a is a constant. What is h'(x)?
a) 1/(a²+x²) b) 2x/(a²+x²) c) a/(a²+x²) d) x/(a²+x²)
Answer: a) 1/(a²+x²)
41. If f(x) = ∫₀ˣ (1/√(1+t³)) dt, then f'(x) =
a) 1/√(1+x³) b) 3x²/√(1+x³) c) 1/(1+x³) d) 3/(1+x³)
Answer: a) 1/√(1+x³)
42. Given F(x) = ∫₀ˣ (t²e^t) dt, what is F'(x)?
a) x²e^x b) 2xe^x c) e^x d) x²e^x + 2xe^x
Answer: a) x²e^x
43. If g(x) = ∫₀ˣ (sin(t)/t²) dt, then g'(x) =
a) cos(x)/x² b) sin(x)/x² c) -sin(x)/x³ d) cos(x)/x
Answer: b) sin(x)/x²
44. Let h(x) = ∫₁ˣ (t ln²(t)) dt. What is h'(x)?
a) ln²(x) b) x ln²(x) c) 2x ln(x) d) 2 ln(x)
Answer: b) x ln²(x)
45. If f(x) = ∫₀ˣ (cos(t²)) dt, then f'(x) =
a) -2x sin(x²) b) cos(x²) c) -sin(x²) d) 2x cos(x²)
Answer: b) cos(x²)
46. Given F(x) = ∫₀ˣ (1/(1+e^t)) dt, what is F'(x)?
a) 1/(1+e^x) b) e^x/(1+e^x) c) 1/(1+e^(-x)) d) e^(-x)/(1+e^(-x))
Answer: a) 1/(1+e^x)
47. If g(x) = ∫₁ˣ (√(t²+1)) dt, then g'(x) =
a) √(x²+1) b) x/√(x²+1) c) 1/√(x²+1) d) x√(x²+1)
Answer: a) √(x²+1)
48. Let h(x) = ∫₀ˣ (t sin(t)) dt. What is h'(x)?
a) sin(x) b) x sin(x) c) cos(x) d) x cos(x)
Answer: b) x sin(x)
49. If f(x) = ∫₀ˣ (e^(-t²)) dt, then f'(x) =
a) -2xe^(-x²) b) e^(-x²) c) -e^(-x²) d) 2xe^(-x²)
Answer: b) e^(-x²)
. Given F(x) = ∫₀ˣ (t ln(t)) dt, what is F'(x)?
a) ln(x) b) x ln(x) c) x + ln(x) d) x ln(x) - x
Answer: b) x ln(x)
35. If g(x) = ∫₁ˣ (1/(1+t³)) dt, then g'(x) =
a) 1/(1+x³) b) 3x²/(1+x³) c) 1/(1+x) d) 3/(1+x³)
Answer: a) 1/(1+x³)
36. Let h(x) = ∫₀ˣ arccos(t) dt. What is h'(x)?
a) -1/√(1-x²) b) 1/√(1-x²) c) arccos(x) d) -arccos(x)
Answer: c) arccos(x)
37. If f(x) = ∫₀ˣ (t/(1+t²)) dt, then f'(x) =
a) 1/(1+x²) b) x/(1+x²) c) arctan(x) d) 2x/(1+x²)
Answer: b) x/(1+x²)
38. Given F(x) = ∫₀ˣ csc(t) dt, what is F'(x)?
a) sec(x) b) csc(x) c) cot(x) d) tan(x)
Answer: b) csc(x)
39. If g(x) = ∫₁ˣ (ln(t)/t) dt, then g'(x) =
a) ln(ln(x)) b) ln(x)/x c) 1/x d) ln²(x)/2
Answer: b) ln(x)/x
40. Let h(x) = ∫₀ˣ (1/(a²+t²)) dt, where a is a constant. What is h'(x)?
a) 1/(a²+x²) b) 2x/(a²+x²) c) a/(a²+x²) d) x/(a²+x²)
Answer: a) 1/(a²+x²)
41. If f(x) = ∫₀ˣ (1/√(1+t³)) dt, then f'(x) =
a) 1/√(1+x³) b) 3x²/√(1+x³) c) 1/(1+x³) d) 3/(1+x³)
Answer: a) 1/√(1+x³)
42. Given F(x) = ∫₀ˣ (t²e^t) dt, what is F'(x)?
a) x²e^x b) 2xe^x c) e^x d) x²e^x + 2xe^x
Answer: a) x²e^x
43. If g(x) = ∫₀ˣ (sin(t)/t²) dt, then g'(x) =
a) cos(x)/x² b) sin(x)/x² c) -sin(x)/x³ d) cos(x)/x
Answer: b) sin(x)/x²
44. Let h(x) = ∫₁ˣ (t ln²(t)) dt. What is h'(x)?
a) ln²(x) b) x ln²(x) c) 2x ln(x) d) 2 ln(x)
Answer: b) x ln²(x)
45. If f(x) = ∫₀ˣ (cos(t²)) dt, then f'(x) =
a) -2x sin(x²) b) cos(x²) c) -sin(x²) d) 2x cos(x²)
Answer: b) cos(x²)
46. Given F(x) = ∫₀ˣ (1/(1+e^t)) dt, what is F'(x)?
a) 1/(1+e^x) b) e^x/(1+e^x) c) 1/(1+e^(-x)) d) e^(-x)/(1+e^(-x))
Answer: a) 1/(1+e^x)
47. If g(x) = ∫₁ˣ (√(t²+1)) dt, then g'(x) =
a) √(x²+1) b) x/√(x²+1) c) 1/√(x²+1) d) x√(x²+1)
Answer: a) √(x²+1)
48. Let h(x) = ∫₀ˣ (t sin(t)) dt. What is h'(x)?
a) sin(x) b) x sin(x) c) cos(x) d) x cos(x)
Answer: b) x sin(x)
49. If f(x) = ∫₀ˣ (e^(-t²)) dt, then f'(x) =
a) -2xe^(-x²) b) e^(-x²) c) -e^(-x²) d) 2xe^(-x²)
Answer: b) e^(-x²)
. Given F(x) = ∫₀ˣ (t ln(t)) dt, what is F'(x)?
a) ln(x) b) x ln(x) c) x + ln(x) d) x ln(x) - x
Answer: b) x ln(x)
35. If g(x) = ∫₁ˣ (1/(1+t³)) dt, then g'(x) =
a) 1/(1+x³) b) 3x²/(1+x³) c) 1/(1+x) d) 3/(1+x³)
Answer: a) 1/(1+x³)
36. Let h(x) = ∫₀ˣ arccos(t) dt. What is h'(x)?
a) -1/√(1-x²) b) 1/√(1-x²) c) arccos(x) d) -arccos(x)
Answer: c) arccos(x)
37. If f(x) = ∫₀ˣ (t/(1+t²)) dt, then f'(x) =
a) 1/(1+x²) b) x/(1+x²) c) arctan(x) d) 2x/(1+x²)
Answer: b) x/(1+x²)
38. Given F(x) = ∫₀ˣ csc(t) dt, what is F'(x)?
a) sec(x) b) csc(x) c) cot(x) d) tan(x)
Answer: b) csc(x)
39. If g(x) = ∫₁ˣ (ln(t)/t) dt, then g'(x) =
a) ln(ln(x)) b) ln(x)/x c) 1/x d) ln²(x)/2
Answer: b) ln(x)/x
40. Let h(x) = ∫₀ˣ (1/(a²+t²)) dt, where a is a constant. What is h'(x)?
a) 1/(a²+x²) b) 2x/(a²+x²) c) a/(a²+x²) d) x/(a²+x²)
Answer: a) 1/(a²+x²)
41. If f(x) = ∫₀ˣ (1/√(1+t³)) dt, then f'(x) =
a) 1/√(1+x³) b) 3x²/√(1+x³) c) 1/(1+x³) d) 3/(1+x³)
Answer: a) 1/√(1+x³)
42. Given F(x) = ∫₀ˣ (t²e^t) dt, what is F'(x)?
a) x²e^x b) 2xe^x c) e^x d) x²e^x + 2xe^x
Answer: a) x²e^x
43. If g(x) = ∫₀ˣ (sin(t)/t²) dt, then g'(x) =
a) cos(x)/x² b) sin(x)/x² c) -sin(x)/x³ d) cos(x)/x
Answer: b) sin(x)/x²
44. Let h(x) = ∫₁ˣ (t ln²(t)) dt. What is h'(x)?
a) ln²(x) b) x ln²(x) c) 2x ln(x) d) 2 ln(x)
Answer: b) x ln²(x)
45. If f(x) = ∫₀ˣ (cos(t²)) dt, then f'(x) =
a) -2x sin(x²) b) cos(x²) c) -sin(x²) d) 2x cos(x²)
Answer: b) cos(x²)
46. Given F(x) = ∫₀ˣ (1/(1+e^t)) dt, what is F'(x)?
a) 1/(1+e^x) b) e^x/(1+e^x) c) 1/(1+e^(-x)) d) e^(-x)/(1+e^(-x))
Answer: a) 1/(1+e^x)
47. If g(x) = ∫₁ˣ (√(t²+1)) dt, then g'(x) =
a) √(x²+1) b) x/√(x²+1) c) 1/√(x²+1) d) x√(x²+1)
Answer: a) √(x²+1)
48. Let h(x) = ∫₀ˣ (t sin(t)) dt. What is h'(x)?
a) sin(x) b) x sin(x) c) cos(x) d) x cos(x)
Answer: b) x sin(x)
49. If f(x) = ∫₀ˣ (e^(-t²)) dt, then f'(x) =
a) -2xe^(-x²) b) e^(-x²) c) -e^(-x²) d) 2xe^(-x²)
Answer: b) e^(-x²)
. Given F(x) = ∫₀ˣ (t ln(t)) dt, what is F'(x)?
a) ln(x) b) x ln(x) c) x + ln(x) d) x ln(x) - x
Answer: b) x ln(x)
35. If g(x) = ∫₁ˣ (1/(1+t³)) dt, then g'(x) =
a) 1/(1+x³) b) 3x²/(1+x³) c) 1/(1+x) d) 3/(1+x³)
Answer: a) 1/(1+x³)
36. Let h(x) = ∫₀ˣ arccos(t) dt. What is h'(x)?
a) -1/√(1-x²) b) 1/√(1-x²) c) arccos(x) d) -arccos(x)
Answer: c) arccos(x)
37. If f(x) = ∫₀ˣ (t/(1+t²)) dt, then f'(x) =
a) 1/(1+x²) b) x/(1+x²) c) arctan(x) d) 2x/(1+x²)
Answer: b) x/(1+x²)
38. Given F(x) = ∫₀ˣ csc(t) dt, what is F'(x)?
a) sec(x) b) csc(x) c) cot(x) d) tan(x)
Answer: b) csc(x)
39. If g(x) = ∫₁ˣ (ln(t)/t) dt, then g'(x) =
a) ln(ln(x)) b) ln(x)/x c) 1/x d) ln²(x)/2
Answer: b) ln(x)/x
40. Let h(x) = ∫₀ˣ (1/(a²+t²)) dt, where a is a constant. What is h'(x)?
a) 1/(a²+x²) b) 2x/(a²+x²) c) a/(a²+x²) d) x/(a²+x²)
Answer: a) 1/(a²+x²)
41. If f(x) = ∫₀ˣ (1/√(1+t³)) dt, then f'(x) =
a) 1/√(1+x³) b) 3x²/√(1+x³) c) 1/(1+x³) d) 3/(1+x³)
Answer: a) 1/√(1+x³)
42. Given F(x) = ∫₀ˣ (t²e^t) dt, what is F'(x)?
a) x²e^x b) 2xe^x c) e^x d) x²e^x + 2xe^x
Answer: a) x²e^x
43. If g(x) = ∫₀ˣ (sin(t)/t²) dt, then g'(x) =
a) cos(x)/x² b) sin(x)/x² c) -sin(x)/x³ d) cos(x)/x
Answer: b) sin(x)/x²
44. Let h(x) = ∫₁ˣ (t ln²(t)) dt. What is h'(x)?
a) ln²(x) b) x ln²(x) c) 2x ln(x) d) 2 ln(x)
Answer: b) x ln²(x)
45. If f(x) = ∫₀ˣ (cos(t²)) dt, then f'(x) =
a) -2x sin(x²) b) cos(x²) c) -sin(x²) d) 2x cos(x²)
Answer: b) cos(x²)
46. Given F(x) = ∫₀ˣ (1/(1+e^t)) dt, what is F'(x)?
a) 1/(1+e^x) b) e^x/(1+e^x) c) 1/(1+e^(-x)) d) e^(-x)/(1+e^(-x))
Answer: a) 1/(1+e^x)
47. If g(x) = ∫₁ˣ (√(t²+1)) dt, then g'(x) =
a) √(x²+1) b) x/√(x²+1) c) 1/√(x²+1) d) x√(x²+1)
Answer: a) √(x²+1)
48. Let h(x) = ∫₀ˣ (t sin(t)) dt. What is h'(x)?
a) sin(x) b) x sin(x) c) cos(x) d) x cos(x)
Answer: b) x sin(x)
49. If f(x) = ∫₀ˣ (e^(-t²)) dt, then f'(x) =
a) -2xe^(-x²) b) e^(-x²) c) -e^(-x²) d) 2xe^(-x²)
Answer: b) e^(-x²)
. Given F(x) = ∫₀ˣ (t ln(t)) dt, what is F'(x)?
a) ln(x) b) x ln(x) c) x + ln(x) d) x ln(x) - x
Answer: b) x ln(x)
35. If g(x) = ∫₁ˣ (1/(1+t³)) dt, then g'(x) =
a) 1/(1+x³) b) 3x²/(1+x³) c) 1/(1+x) d) 3/(1+x³)
Answer: a) 1/(1+x³)
36. Let h(x) = ∫₀ˣ arccos(t) dt. What is h'(x)?
a) -1/√(1-x²) b) 1/√(1-x²) c) arccos(x) d) -arccos(x)
Answer: c) arccos(x)
37. If f(x) = ∫₀ˣ (t/(1+t²)) dt, then f'(x) =
a) 1/(1+x²) b) x/(1+x²) c) arctan(x) d) 2x/(1+x²)
Answer: b) x/(1+x²)
38. Given F(x) = ∫₀ˣ csc(t) dt, what is F'(x)?
a) sec(x) b) csc(x) c) cot(x) d) tan(x)
Answer: b) csc(x)
39. If g(x) = ∫₁ˣ (ln(t)/t) dt, then g'(x) =
a) ln(ln(x)) b) ln(x)/x c) 1/x d) ln²(x)/2
Answer: b) ln(x)/x
40. Let h(x) = ∫₀ˣ (1/(a²+t²)) dt, where a is a constant. What is h'(x)?
a) 1/(a²+x²) b) 2x/(a²+x²) c) a/(a²+x²) d) x/(a²+x²)
Answer: a) 1/(a²+x²)
41. If f(x) = ∫₀ˣ (1/√(1+t³)) dt, then f'(x) =
a) 1/√(1+x³) b) 3x²/√(1+x³) c) 1/(1+x³) d) 3/(1+x³)
Answer: a) 1/√(1+x³)
42. Given F(x) = ∫₀ˣ (t²e^t) dt, what is F'(x)?
a) x²e^x b) 2xe^x c) e^x d) x²e^x + 2xe^x
Answer: a) x²e^x
43. If g(x) = ∫₀ˣ (sin(t)/t²) dt, then g'(x) =
a) cos(x)/x² b) sin(x)/x² c) -sin(x)/x³ d) cos(x)/x
Answer: b) sin(x)/x²
44. Let h(x) = ∫₁ˣ (t ln²(t)) dt. What is h'(x)?
a) ln²(x) b) x ln²(x) c) 2x ln(x) d) 2 ln(x)
Answer: b) x ln²(x)
45. If f(x) = ∫₀ˣ (cos(t²)) dt, then f'(x) =
a) -2x sin(x²) b) cos(x²) c) -sin(x²) d) 2x cos(x²)
Answer: b) cos(x²)
46. Given F(x) = ∫₀ˣ (1/(1+e^t)) dt, what is F'(x)?
a) 1/(1+e^x) b) e^x/(1+e^x) c) 1/(1+e^(-x)) d) e^(-x)/(1+e^(-x))
Answer: a) 1/(1+e^x)
47. If g(x) = ∫₁ˣ (√(t²+1)) dt, then g'(x) =
a) √(x²+1) b) x/√(x²+1) c) 1/√(x²+1) d) x√(x²+1)
Answer: a) √(x²+1)
48. Let h(x) = ∫₀ˣ (t sin(t)) dt. What is h'(x)?
a) sin(x) b) x sin(x) c) cos(x) d) x cos(x)
Answer: b) x sin(x)
49. If f(x) = ∫₀ˣ (e^(-t²)) dt, then f'(x) =
a) -2xe^(-x²) b) e^(-x²) c) -e^(-x²) d) 2xe^(-x²)
Answer: b) e^(-x²)
. Given F(x) = ∫₀ˣ (t ln(t)) dt, what is F'(x)?
a) ln(x) b) x ln(x) c) x + ln(x) d) x ln(x) - x
Answer: b) x ln(x)
35. If g(x) = ∫₁ˣ (1/(1+t³)) dt, then g'(x) =
a) 1/(1+x³) b) 3x²/(1+x³) c) 1/(1+x) d) 3/(1+x³)
Answer: a) 1/(1+x³)
36. Let h(x) = ∫₀ˣ arccos(t) dt. What is h'(x)?
a) -1/√(1-x²) b) 1/√(1-x²) c) arccos(x) d) -arccos(x)
Answer: c) arccos(x)
37. If f(x) = ∫₀ˣ (t/(1+t²)) dt, then f'(x) =
a) 1/(1+x²) b) x/(1+x²) c) arctan(x) d) 2x/(1+x²)
Answer: b) x/(1+x²)
38. Given F(x) = ∫₀ˣ csc(t) dt, what is F'(x)?
a) sec(x) b) csc(x) c) cot(x) d) tan(x)
Answer: b) csc(x)
39. If g(x) = ∫₁ˣ (ln(t)/t) dt, then g'(x) =
a) ln(ln(x)) b) ln(x)/x c) 1/x d) ln²(x)/2
Answer: b) ln(x)/x
40. Let h(x) = ∫₀ˣ (1/(a²+t²)) dt, where a is a constant. What is h'(x)?
a) 1/(a²+x²) b) 2x/(a²+x²) c) a/(a²+x²) d) x/(a²+x²)
Answer: a) 1/(a²+x²)
41. If f(x) = ∫₀ˣ (1/√(1+t³)) dt, then f'(x) =
a) 1/√(1+x³) b) 3x²/√(1+x³) c) 1/(1+x³) d) 3/(1+x³)
Answer: a) 1/√(1+x³)
42. Given F(x) = ∫₀ˣ (t²e^t) dt, what is F'(x)?
a) x²e^x b) 2xe^x c) e^x d) x²e^x + 2xe^x
Answer: a) x²e^x
43. If g(x) = ∫₀ˣ (sin(t)/t²) dt, then g'(x) =
a) cos(x)/x² b) sin(x)/x² c) -sin(x)/x³ d) cos(x)/x
Answer: b) sin(x)/x²
44. Let h(x) = ∫₁ˣ (t ln²(t)) dt. What is h'(x)?
a) ln²(x) b) x ln²(x) c) 2x ln(x) d) 2 ln(x)
Answer: b) x ln²(x)
45. If f(x) = ∫₀ˣ (cos(t²)) dt, then f'(x) =
a) -2x sin(x²) b) cos(x²) c) -sin(x²) d) 2x cos(x²)
Answer: b) cos(x²)
46. Given F(x) = ∫₀ˣ (1/(1+e^t)) dt, what is F'(x)?
a) 1/(1+e^x) b) e^x/(1+e^x) c) 1/(1+e^(-x)) d) e^(-x)/(1+e^(-x))
Answer: a) 1/(1+e^x)
47. If g(x) = ∫₁ˣ (√(t²+1)) dt, then g'(x) =
a) √(x²+1) b) x/√(x²+1) c) 1/√(x²+1) d) x√(x²+1)
Answer: a) √(x²+1)
48. Let h(x) = ∫₀ˣ (t sin(t)) dt. What is h'(x)?
a) sin(x) b) x sin(x) c) cos(x) d) x cos(x)
Answer: b) x sin(x)
49. If f(x) = ∫₀ˣ (e^(-t²)) dt, then f'(x) =
a) -2xe^(-x²) b) e^(-x²) c) -e^(-x²) d) 2xe^(-x²)
Answer: b) e^(-x²)
. Given F(x) = ∫₀ˣ (t ln(t)) dt, what is F'(x)?
a) ln(x) b) x ln(x) c) x + ln(x) d) x ln(x) - x
Answer: b) x ln(x)
35. If g(x) = ∫₁ˣ (1/(1+t³)) dt, then g'(x) =
a) 1/(1+x³) b) 3x²/(1+x³) c) 1/(1+x) d) 3/(1+x³)
Answer: a) 1/(1+x³)
36. Let h(x) = ∫₀ˣ arccos(t) dt. What is h'(x)?
a) -1/√(1-x²) b) 1/√(1-x²) c) arccos(x) d) -arccos(x)
Answer: c) arccos(x)
37. If f(x) = ∫₀ˣ (t/(1+t²)) dt, then f'(x) =
a) 1/(1+x²) b) x/(1+x²) c) arctan(x) d) 2x/(1+x²)
Answer: b) x/(1+x²)
38. Given F(x) = ∫₀ˣ csc(t) dt, what is F'(x)?
a) sec(x) b) csc(x) c) cot(x) d) tan(x)
Answer: b) csc(x)
39. If g(x) = ∫₁ˣ (ln(t)/t) dt, then g'(x) =
a) ln(ln(x)) b) ln(x)/x c) 1/x d) ln²(x)/2
Answer: b) ln(x)/x
40. Let h(x) = ∫₀ˣ (1/(a²+t²)) dt, where a is a constant. What is h'(x)?
a) 1/(a²+x²) b) 2x/(a²+x²) c) a/(a²+x²) d) x/(a²+x²)
Answer: a) 1/(a²+x²)
41. If f(x) = ∫₀ˣ (1/√(1+t³)) dt, then f'(x) =
a) 1/√(1+x³) b) 3x²/√(1+x³) c) 1/(1+x³) d) 3/(1+x³)
Answer: a) 1/√(1+x³)
42. Given F(x) = ∫₀ˣ (t²e^t) dt, what is F'(x)?
a) x²e^x b) 2xe^x c) e^x d) x²e^x + 2xe^x
Answer: a) x²e^x
43. If g(x) = ∫₀ˣ (sin(t)/t²) dt, then g'(x) =
a) cos(x)/x² b) sin(x)/x² c) -sin(x)/x³ d) cos(x)/x
Answer: b) sin(x)/x²
44. Let h(x) = ∫₁ˣ (t ln²(t)) dt. What is h'(x)?
a) ln²(x) b) x ln²(x) c) 2x ln(x) d) 2 ln(x)
Answer: b) x ln²(x)
45. If f(x) = ∫₀ˣ (cos(t²)) dt, then f'(x) =
a) -2x sin(x²) b) cos(x²) c) -sin(x²) d) 2x cos(x²)
Answer: b) cos(x²)
46. Given F(x) = ∫₀ˣ (1/(1+e^t)) dt, what is F'(x)?
a) 1/(1+e^x) b) e^x/(1+e^x) c) 1/(1+e^(-x)) d) e^(-x)/(1+e^(-x))
Answer: a) 1/(1+e^x)
47. If g(x) = ∫₁ˣ (√(t²+1)) dt, then g'(x) =
a) √(x²+1) b) x/√(x²+1) c) 1/√(x²+1) d) x√(x²+1)
Answer: a) √(x²+1)
48. Let h(x) = ∫₀ˣ (t sin(t)) dt. What is h'(x)?
a) sin(x) b) x sin(x) c) cos(x) d) x cos(x)
Answer: b) x sin(x)
49. If f(x) = ∫₀ˣ (e^(-t²)) dt, then f'(x) =
a) -2xe^(-x²) b) e^(-x²) c) -e^(-x²) d) 2xe^(-x²)
Answer: b) e^(-x²)
. Given F(x) = ∫₀ˣ (t ln(t)) dt, what is F'(x)?
a) ln(x) b) x ln(x) c) x + ln(x) d) x ln(x) - x
Answer: b) x ln(x)
35. If g(x) = ∫₁ˣ (1/(1+t³)) dt, then g'(x) =
a) 1/(1+x³) b) 3x²/(1+x³) c) 1/(1+x) d) 3/(1+x³)
Answer: a) 1/(1+x³)
36. Let h(x) = ∫₀ˣ arccos(t) dt. What is h'(x)?
a) -1/√(1-x²) b) 1/√(1-x²) c) arccos(x) d) -arccos(x)
Answer: c) arccos(x)
37. If f(x) = ∫₀ˣ (t/(1+t²)) dt, then f'(x) =
a) 1/(1+x²) b) x/(1+x²) c) arctan(x) d) 2x/(1+x²)
Answer: b) x/(1+x²)
38. Given F(x) = ∫₀ˣ csc(t) dt, what is F'(x)?
a) sec(x) b) csc(x) c) cot(x) d) tan(x)
Answer: b) csc(x)
39. If g(x) = ∫₁ˣ (ln(t)/t) dt, then g'(x) =
a) ln(ln(x)) b) ln(x)/x c) 1/x d) ln²(x)/2
Answer: b) ln(x)/x
40. Let h(x) = ∫₀ˣ (1/(a²+t²)) dt, where a is a constant. What is h'(x)?
a) 1/(a²+x²) b) 2x/(a²+x²) c) a/(a²+x²) d) x/(a²+x²)
Answer: a) 1/(a²+x²)
41. If f(x) = ∫₀ˣ (1/√(1+t³)) dt, then f'(x) =
a) 1/√(1+x³) b) 3x²/√(1+x³) c) 1/(1+x³) d) 3/(1+x³)
Answer: a) 1/√(1+x³)
42. Given F(x) = ∫₀ˣ (t²e^t) dt, what is F'(x)?
a) x²e^x b) 2xe^x c) e^x d) x²e^x + 2xe^x
Answer: a) x²e^x
43. If g(x) = ∫₀ˣ (sin(t)/t²) dt, then g'(x) =
a) cos(x)/x² b) sin(x)/x² c) -sin(x)/x³ d) cos(x)/x
Answer: b) sin(x)/x²
44. Let h(x) = ∫₁ˣ (t ln²(t)) dt. What is h'(x)?
a) ln²(x) b) x ln²(x) c) 2x ln(x) d) 2 ln(x)
Answer: b) x ln²(x)
45. If f(x) = ∫₀ˣ (cos(t²)) dt, then f'(x) =
a) -2x sin(x²) b) cos(x²) c) -sin(x²) d) 2x cos(x²)
Answer: b) cos(x²)
46. Given F(x) = ∫₀ˣ (1/(1+e^t)) dt, what is F'(x)?
a) 1/(1+e^x) b) e^x/(1+e^x) c) 1/(1+e^(-x)) d) e^(-x)/(1+e^(-x))
Answer: a) 1/(1+e^x)
47. If g(x) = ∫₁ˣ (√(t²+1)) dt, then g'(x) =
a) √(x²+1) b) x/√(x²+1) c) 1/√(x²+1) d) x√(x²+1)
Answer: a) √(x²+1)
48. Let h(x) = ∫₀ˣ (t sin(t)) dt. What is h'(x)?
a) sin(x) b) x sin(x) c) cos(x) d) x cos(x)
Answer: b) x sin(x)
49. If f(x) = ∫₀ˣ (e^(-t²)) dt, then f'(x) =
a) -2xe^(-x²) b) e^(-x²) c) -e^(-x²) d) 2xe^(-x²)
Answer: b) e^(-x²)
. Given F(x) = ∫₀ˣ (t ln(t)) dt, what is F'(x)?
a) ln(x) b) x ln(x) c) x + ln(x) d) x ln(x) - x
Answer: b) x ln(x)
35. If g(x) = ∫₁ˣ (1/(1+t³)) dt, then g'(x) =
a) 1/(1+x³) b) 3x²/(1+x³) c) 1/(1+x) d) 3/(1+x³)
Answer: a) 1/(1+x³)
36. Let h(x) = ∫₀ˣ arccos(t) dt. What is h'(x)?
a) -1/√(1-x²) b) 1/√(1-x²) c) arccos(x) d) -arccos(x)
Answer: c) arccos(x)
37. If f(x) = ∫₀ˣ (t/(1+t²)) dt, then f'(x) =
a) 1/(1+x²) b) x/(1+x²) c) arctan(x) d) 2x/(1+x²)
Answer: b) x/(1+x²)
38. Given F(x) = ∫₀ˣ csc(t) dt, what is F'(x)?
a) sec(x) b) csc(x) c) cot(x) d) tan(x)
Answer: b) csc(x)
39. If g(x) = ∫₁ˣ (ln(t)/t) dt, then g'(x) =
a) ln(ln(x)) b) ln(x)/x c) 1/x d) ln²(x)/2
Answer: b) ln(x)/x
40. Let h(x) = ∫₀ˣ (1/(a²+t²)) dt, where a is a constant. What is h'(x)?
a) 1/(a²+x²) b) 2x/(a²+x²) c) a/(a²+x²) d) x/(a²+x²)
Answer: a) 1/(a²+x²)
41. If f(x) = ∫₀ˣ (1/√(1+t³)) dt, then f'(x) =
a) 1/√(1+x³) b) 3x²/√(1+x³) c) 1/(1+x³) d) 3/(1+x³)
Answer: a) 1/√(1+x³)
42. Given F(x) = ∫₀ˣ (t²e^t) dt, what is F'(x)?
a) x²e^x b) 2xe^x c) e^x d) x²e^x + 2xe^x
Answer: a) x²e^x
43. If g(x) = ∫₀ˣ (sin(t)/t²) dt, then g'(x) =
a) cos(x)/x² b) sin(x)/x² c) -sin(x)/x³ d) cos(x)/x
Answer: b) sin(x)/x²
44. Let h(x) = ∫₁ˣ (t ln²(t)) dt. What is h'(x)?
a) ln²(x) b) x ln²(x) c) 2x ln(x) d) 2 ln(x)
Answer: b) x ln²(x)
45. If f(x) = ∫₀ˣ (cos(t²)) dt, then f'(x) =
a) -2x sin(x²) b) cos(x²) c) -sin(x²) d) 2x cos(x²)
Answer: b) cos(x²)
46. Given F(x) = ∫₀ˣ (1/(1+e^t)) dt, what is F'(x)?
a) 1/(1+e^x) b) e^x/(1+e^x) c) 1/(1+e^(-x)) d) e^(-x)/(1+e^(-x))
Answer: a) 1/(1+e^x)
47. If g(x) = ∫₁ˣ (√(t²+1)) dt, then g'(x) =
a) √(x²+1) b) x/√(x²+1) c) 1/√(x²+1) d) x√(x²+1)
Answer: a) √(x²+1)
48. Let h(x) = ∫₀ˣ (t sin(t)) dt. What is h'(x)?
a) sin(x) b) x sin(x) c) cos(x) d) x cos(x)
Answer: b) x sin(x)
49. If f(x) = ∫₀ˣ (e^(-t²)) dt, then f'(x) =
a) -2xe^(-x²) b) e^(-x²) c) -e^(-x²) d) 2xe^(-x²)
Answer: b) e^(-x²)
. Given F(x) = ∫₀ˣ (t ln(t)) dt, what is F'(x)?
a) ln(x) b) x ln(x) c) x + ln(x) d) x ln(x) - x
Answer: b) x ln(x)
35. If g(x) = ∫₁ˣ (1/(1+t³)) dt, then g'(x) =
a) 1/(1+x³) b) 3x²/(1+x³) c) 1/(1+x) d) 3/(1+x³)
Answer: a) 1/(1+x³)
36. Let h(x) = ∫₀ˣ arccos(t) dt. What is h'(x)?
a) -1/√(1-x²) b) 1/√(1-x²) c) arccos(x) d) -arccos(x)
Answer: c) arccos(x)
37. If f(x) = ∫₀ˣ (t/(1+t²)) dt, then f'(x) =
a) 1/(1+x²) b) x/(1+x²) c) arctan(x) d) 2x/(1+x²)
Answer: b) x/(1+x²)
38. Given F(x) = ∫₀ˣ csc(t) dt, what is F'(x)?
a) sec(x) b) csc(x) c) cot(x) d) tan(x)
Answer: b) csc(x)
39. If g(x) = ∫₁ˣ (ln(t)/t) dt, then g'(x) =
a) ln(ln(x)) b) ln(x)/x c) 1/x d) ln²(x)/2
Answer: b) ln(x)/x
40. Let h(x) = ∫₀ˣ (1/(a²+t²)) dt, where a is a constant. What is h'(x)?
a) 1/(a²+x²) b) 2x/(a²+x²) c) a/(a²+x²) d) x/(a²+x²)
Answer: a) 1/(a²+x²)
41. If f(x) = ∫₀ˣ (1/√(1+t³)) dt, then f'(x) =
a) 1/√(1+x³) b) 3x²/√(1+x³) c) 1/(1+x³) d) 3/(1+x³)
Answer: a) 1/√(1+x³)
42. Given F(x) = ∫₀ˣ (t²e^t) dt, what is F'(x)?
a) x²e^x b) 2xe^x c) e^x d) x²e^x + 2xe^x
Answer: a) x²e^x
43. If g(x) = ∫₀ˣ (sin(t)/t²) dt, then g'(x) =
a) cos(x)/x² b) sin(x)/x² c) -sin(x)/x³ d) cos(x)/x
Answer: b) sin(x)/x²
44. Let h(x) = ∫₁ˣ (t ln²(t)) dt. What is h'(x)?
a) ln²(x) b) x ln²(x) c) 2x ln(x) d) 2 ln(x)
Answer: b) x ln²(x)
45. If f(x) = ∫₀ˣ (cos(t²)) dt, then f'(x) =
a) -2x sin(x²) b) cos(x²) c) -sin(x²) d) 2x cos(x²)
Answer: b) cos(x²)
46. Given F(x) = ∫₀ˣ (1/(1+e^t)) dt, what is F'(x)?
a) 1/(1+e^x) b) e^x/(1+e^x) c) 1/(1+e^(-x)) d) e^(-x)/(1+e^(-x))
Answer: a) 1/(1+e^x)
47. If g(x) = ∫₁ˣ (√(t²+1)) dt, then g'(x) =
a) √(x²+1) b) x/√(x²+1) c) 1/√(x²+1) d) x√(x²+1)
Answer: a) √(x²+1)
48. Let h(x) = ∫₀ˣ (t sin(t)) dt. What is h'(x)?
a) sin(x) b) x sin(x) c) cos(x) d) x cos(x)
Answer: b) x sin(x)
49. If f(x) = ∫₀ˣ (e^(-t²)) dt, then f'(x) =
a) -2xe^(-x²) b) e^(-x²) c) -e^(-x²) d) 2xe^(-x²)
Answer: b) e^(-x²)
. Given F(x) = ∫₀ˣ (t ln(t)) dt, what is F'(x)?
a) ln(x) b) x ln(x) c) x + ln(x) d) x ln(x) - x
Answer: b) x ln(x)
35. If g(x) = ∫₁ˣ (1/(1+t³)) dt, then g'(x) =
a) 1/(1+x³) b) 3x²/(1+x³) c) 1/(1+x) d) 3/(1+x³)
Answer: a) 1/(1+x³)
36. Let h(x) = ∫₀ˣ arccos(t) dt. What is h'(x)?
a) -1/√(1-x²) b) 1/√(1-x²) c) arccos(x) d) -arccos(x)
Answer: c) arccos(x)
37. If f(x) = ∫₀ˣ (t/(1+t²)) dt, then f'(x) =
a) 1/(1+x²) b) x/(1+x²) c) arctan(x) d) 2x/(1+x²)
Answer: b) x/(1+x²)
38. Given F(x) = ∫₀ˣ csc(t) dt, what is F'(x)?
a) sec(x) b) csc(x) c) cot(x) d) tan(x)
Answer: b) csc(x)
39. If g(x) = ∫₁ˣ (ln(t)/t) dt, then g'(x) =
a) ln(ln(x)) b) ln(x)/x c) 1/x d) ln²(x)/2
Answer: b) ln(x)/x
40. Let h(x) = ∫₀ˣ (1/(a²+t²)) dt, where a is a constant. What is h'(x)?
a) 1/(a²+x²) b) 2x/(a²+x²) c) a/(a²+x²) d) x/(a²+x²)
Answer: a) 1/(a²+x²)
41. If f(x) = ∫₀ˣ (1/√(1+t³)) dt, then f'(x) =
a) 1/√(1+x³) b) 3x²/√(1+x³) c) 1/(1+x³) d) 3/(1+x³)
Answer: a) 1/√(1+x³)
42. Given F(x) = ∫₀ˣ (t²e^t) dt, what is F'(x)?
a) x²e^x b) 2xe^x c) e^x d) x²e^x + 2xe^x
Answer: a) x²e^x
43. If g(x) = ∫₀ˣ (sin(t)/t²) dt, then g'(x) =
a) cos(x)/x² b) sin(x)/x² c) -sin(x)/x³ d) cos(x)/x
Answer: b) sin(x)/x²
44. Let h(x) = ∫₁ˣ (t ln²(t)) dt. What is h'(x)?
a) ln²(x) b) x ln²(x) c) 2x ln(x) d) 2 ln(x)
Answer: b) x ln²(x)
45. If f(x) = ∫₀ˣ (cos(t²)) dt, then f'(x) =
a) -2x sin(x²) b) cos(x²) c) -sin(x²) d) 2x cos(x²)
Answer: b) cos(x²)
46. Given F(x) = ∫₀ˣ (1/(1+e^t)) dt, what is F'(x)?
a) 1/(1+e^x) b) e^x/(1+e^x) c) 1/(1+e^(-x)) d) e^(-x)/(1+e^(-x))
Answer: a) 1/(1+e^x)
47. If g(x) = ∫₁ˣ (√(t²+1)) dt, then g'(x) =
a) √(x²+1) b) x/√(x²+1) c) 1/√(x²+1) d) x√(x²+1)
Answer: a) √(x²+1)
48. Let h(x) = ∫₀ˣ (t sin(t)) dt. What is h'(x)?
a) sin(x) b) x sin(x) c) cos(x) d) x cos(x)
Answer: b) x sin(x)
49. If f(x) = ∫₀ˣ (e^(-t²)) dt, then f'(x) =
a) -2xe^(-x²) b) e^(-x²) c) -e^(-x²) d) 2xe^(-x²)
Answer: b) e^(-x²)
. Given F(x) = ∫₀ˣ (t ln(t)) dt, what is F'(x)?
a) ln(x) b) x ln(x) c) x + ln(x) d) x ln(x) - x
Answer: b) x ln(x)
35. If g(x) = ∫₁ˣ (1/(1+t³)) dt, then g'(x) =
a) 1/(1+x³) b) 3x²/(1+x³) c) 1/(1+x) d) 3/(1+x³)
Answer: a) 1/(1+x³)
36. Let h(x) = ∫₀ˣ arccos(t) dt. What is h'(x)?
a) -1/√(1-x²) b) 1/√(1-x²) c) arccos(x) d) -arccos(x)
Answer: c) arccos(x)
37. If f(x) = ∫₀ˣ (t/(1+t²)) dt, then f'(x) =
a) 1/(1+x²) b) x/(1+x²) c) arctan(x) d) 2x/(1+x²)
Answer: b) x/(1+x²)
38. Given F(x) = ∫₀ˣ csc(t) dt, what is F'(x)?
a) sec(x) b) csc(x) c) cot(x) d) tan(x)
Answer: b) csc(x)
39. If g(x) = ∫₁ˣ (ln(t)/t) dt, then g'(x) =
a) ln(ln(x)) b) ln(x)/x c) 1/x d) ln²(x)/2
Answer: b) ln(x)/x
40. Let h(x) = ∫₀ˣ (1/(a²+t²)) dt, where a is a constant. What is h'(x)?
a) 1/(a²+x²) b) 2x/(a²+x²) c) a/(a²+x²) d) x/(a²+x²)
Answer: a) 1/(a²+x²)
41. If f(x) = ∫₀ˣ (1/√(1+t³)) dt, then f'(x) =
a) 1/√(1+x³) b) 3x²/√(1+x³) c) 1/(1+x³) d) 3/(1+x³)
Answer: a) 1/√(1+x³)
42. Given F(x) = ∫₀ˣ (t²e^t) dt, what is F'(x)?
a) x²e^x b) 2xe^x c) e^x d) x²e^x + 2xe^x
Answer: a) x²e^x
43. If g(x) = ∫₀ˣ (sin(t)/t²) dt, then g'(x) =
a) cos(x)/x² b) sin(x)/x² c) -sin(x)/x³ d) cos(x)/x
Answer: b) sin(x)/x²
44. Let h(x) = ∫₁ˣ (t ln²(t)) dt. What is h'(x)?
a) ln²(x) b) x ln²(x) c) 2x ln(x) d) 2 ln(x)
Answer: b) x ln²(x)
45. If f(x) = ∫₀ˣ (cos(t²)) dt, then f'(x) =
a) -2x sin(x²) b) cos(x²) c) -sin(x²) d) 2x cos(x²)
Answer: b) cos(x²)
46. Given F(x) = ∫₀ˣ (1/(1+e^t)) dt, what is F'(x)?
a) 1/(1+e^x) b) e^x/(1+e^x) c) 1/(1+e^(-x)) d) e^(-x)/(1+e^(-x))
Answer: a) 1/(1+e^x)
47. If g(x) = ∫₁ˣ (√(t²+1)) dt, then g'(x) =
a) √(x²+1) b) x/√(x²+1) c) 1/√(x²+1) d) x√(x²+1)
Answer: a) √(x²+1)
48. Let h(x) = ∫₀ˣ (t sin(t)) dt. What is h'(x)?
a) sin(x) b) x sin(x) c) cos(x) d) x cos(x)
Answer: b) x sin(x)
49. If f(x) = ∫₀ˣ (e^(-t²)) dt, then f'(x) =
a) -2xe^(-x²) b) e^(-x²) c) -e^(-x²) d) 2xe^(-x²)
Answer: b) e^(-x²)
. Given F(x) = ∫₀ˣ (t ln(t)) dt, what is F'(x)?
a) ln(x) b) x ln(x) c) x + ln(x) d) x ln(x) - x
Answer: b) x ln(x)
35. If g(x) = ∫₁ˣ (1/(1+t³)) dt, then g'(x) =
a) 1/(1+x³) b) 3x²/(1+x³) c) 1/(1+x) d) 3/(1+x³)
Answer: a) 1/(1+x³)
36. Let h(x) = ∫₀ˣ arccos(t) dt. What is h'(x)?
a) -1/√(1-x²) b) 1/√(1-x²) c) arccos(x) d) -arccos(x)
Answer: c) arccos(x)
37. If f(x) = ∫₀ˣ (t/(1+t²)) dt, then f'(x) =
a) 1/(1+x²) b) x/(1+x²) c) arctan(x) d) 2x/(1+x²)
Answer: b) x/(1+x²)
38. Given F(x) = ∫₀ˣ csc(t) dt, what is F'(x)?
a) sec(x) b) csc(x) c) cot(x) d) tan(x)
Answer: b) csc(x)
39. If g(x) = ∫₁ˣ (ln(t)/t) dt, then g'(x) =
a) ln(ln(x)) b) ln(x)/x c) 1/x d) ln²(x)/2
Answer: b) ln(x)/x
40. Let h(x) = ∫₀ˣ (1/(a²+t²)) dt, where a is a constant. What is h'(x)?
a) 1/(a²+x²) b) 2x/(a²+x²) c) a/(a²+x²) d) x/(a²+x²)
Answer: a) 1/(a²+x²)
41. If f(x) = ∫₀ˣ (1/√(1+t³)) dt, then f'(x) =
a) 1/√(1+x³) b) 3x²/√(1+x³) c) 1/(1+x³) d) 3/(1+x³)
Answer: a) 1/√(1+x³)
42. Given F(x) = ∫₀ˣ (t²e^t) dt, what is F'(x)?
a) x²e^x b) 2xe^x c) e^x d) x²e^x + 2xe^x
Answer: a) x²e^x
43. If g(x) = ∫₀ˣ (sin(t)/t²) dt, then g'(x) =
a) cos(x)/x² b) sin(x)/x² c) -sin(x)/x³ d) cos(x)/x
Answer: b) sin(x)/x²
44. Let h(x) = ∫₁ˣ (t ln²(t)) dt. What is h'(x)?
a) ln²(x) b) x ln²(x) c) 2x ln(x) d) 2 ln(x)
Answer: b) x ln²(x)
45. If f(x) = ∫₀ˣ (cos(t²)) dt, then f'(x) =
a) -2x sin(x²) b) cos(x²) c) -sin(x²) d) 2x cos(x²)
Answer: b) cos(x²)
46. Given F(x) = ∫₀ˣ (1/(1+e^t)) dt, what is F'(x)?
a) 1/(1+e^x) b) e^x/(1+e^x) c) 1/(1+e^(-x)) d) e^(-x)/(1+e^(-x))
Answer: a) 1/(1+e^x)
47. If g(x) = ∫₁ˣ (√(t²+1)) dt, then g'(x) =
a) √(x²+1) b) x/√(x²+1) c) 1/√(x²+1) d) x√(x²+1)
Answer: a) √(x²+1)
48. Let h(x) = ∫₀ˣ (t sin(t)) dt. What is h'(x)?
a) sin(x) b) x sin(x) c) cos(x) d) x cos(x)
Answer: b) x sin(x)
49. If f(x) = ∫₀ˣ (e^(-t²)) dt, then f'(x) =
a) -2xe^(-x²) b) e^(-x²) c) -e^(-x²) d) 2xe^(-x²)
Answer: b) e^(-x²)
. Given F(x) = ∫₀ˣ (t ln(t)) dt, what is F'(x)?
a) ln(x) b) x ln(x) c) x + ln(x) d) x ln(x) - x
Answer: b) x ln(x)
35. If g(x) = ∫₁ˣ (1/(1+t³)) dt, then g'(x) =
a) 1/(1+x³) b) 3x²/(1+x³) c) 1/(1+x) d) 3/(1+x³)
Answer: a) 1/(1+x³)
36. Let h(x) = ∫₀ˣ arccos(t) dt. What is h'(x)?
a) -1/√(1-x²) b) 1/√(1-x²) c) arccos(x) d) -arccos(x)
Answer: c) arccos(x)
37. If f(x) = ∫₀ˣ (t/(1+t²)) dt, then f'(x) =
a) 1/(1+x²) b) x/(1+x²) c) arctan(x) d) 2x/(1+x²)
Answer: b) x/(1+x²)
38. Given F(x) = ∫₀ˣ csc(t) dt, what is F'(x)?
a) sec(x) b) csc(x) c) cot(x) d) tan(x)
Answer: b) csc(x)
39. If g(x) = ∫₁ˣ (ln(t)/t) dt, then g'(x) =
a) ln(ln(x)) b) ln(x)/x c) 1/x d) ln²(x)/2
Answer: b) ln(x)/x
40. Let h(x) = ∫₀ˣ (1/(a²+t²)) dt, where a is a constant. What is h'(x)?
a) 1/(a²+x²) b) 2x/(a²+x²) c) a/(a²+x²) d) x/(a²+x²)
Answer: a) 1/(a²+x²)
41. If f(x) = ∫₀ˣ (1/√(1+t³)) dt, then f'(x) =
a) 1/√(1+x³) b) 3x²/√(1+x³) c) 1/(1+x³) d) 3/(1+x³)
Answer: a) 1/√(1+x³)
42. Given F(x) = ∫₀ˣ (t²e^t) dt, what is F'(x)?
a) x²e^x b) 2xe^x c) e^x d) x²e^x + 2xe^x
Answer: a) x²e^x
43. If g(x) = ∫₀ˣ (sin(t)/t²) dt, then g'(x) =
a) cos(x)/x² b) sin(x)/x² c) -sin(x)/x³ d) cos(x)/x
Answer: b) sin(x)/x²
44. Let h(x) = ∫₁ˣ (t ln²(t)) dt. What is h'(x)?
a) ln²(x) b) x ln²(x) c) 2x ln(x) d) 2 ln(x)
Answer: b) x ln²(x)
45. If f(x) = ∫₀ˣ (cos(t²)) dt, then f'(x) =
a) -2x sin(x²) b) cos(x²) c) -sin(x²) d) 2x cos(x²)
Answer: b) cos(x²)
46. Given F(x) = ∫₀ˣ (1/(1+e^t)) dt, what is F'(x)?
a) 1/(1+e^x) b) e^x/(1+e^x) c) 1/(1+e^(-x)) d) e^(-x)/(1+e^(-x))
Answer: a) 1/(1+e^x)
47. If g(x) = ∫₁ˣ (√(t²+1)) dt, then g'(x) =
a) √(x²+1) b) x/√(x²+1) c) 1/√(x²+1) d) x√(x²+1)
Answer: a) √(x²+1)
48. Let h(x) = ∫₀ˣ (t sin(t)) dt. What is h'(x)?
a) sin(x) b) x sin(x) c) cos(x) d) x cos(x)
Answer: b) x sin(x)
49. If f(x) = ∫₀ˣ (e^(-t²)) dt, then f'(x) =
a) -2xe^(-x²) b) e^(-x²) c) -e^(-x²) d) 2xe^(-x²)
Answer: b) e^(-x²)
50. Given F(x) = ∫₀ˣ (ln(1+t)) dt, what is F'(x)?
a) 1/(1+x) b) ln(1+x) c) x/(1+x) d) ln(x)
Answer
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