Mastery Test Review Form MAT 265
Answers appear in red. 45 questions.
Differentiate the following functions find
“(i.e., 𝒅𝒚
𝒅𝒙 )”
Section 2.3 Basic Derivative Formulas Power Rule and sine and cosine functions –
1.
𝑦= 7 sin 𝑥+ 12 tan 𝑥 − 𝑥3
2. 𝑦=𝑥6.5 −1
𝑥7.5
3. 𝑦= tan (𝑒𝜋)
4. 𝑦=√7𝑥+√5𝑥
5. 𝑦= 3 + 8
𝑥+410
𝑥2
6. 𝑦= √𝑥9
4+ 2√𝑥5
Section 2.4 Product Rule, Quotient Rule (to include other 4 trig functions)
7. 𝑦= tan 𝑥− 11 csc 𝑥
8. 𝑦= cos 𝑥+ cot 𝑥
9. 𝑦=1
sec (𝑥)
10. 𝑦=√𝑥−5
√𝑥+6
11. 𝑦=tan(𝑥)
6𝑥sec(𝑥)
12. 𝑦=csc 𝑥
4+𝑥5
MAT 265 Mastery Exam Review NO CALCULATORS Page 2 of 5
Section 2.5 Chain Rule
13. 𝑦=(3𝑥+ 4)5(6𝑥+ 7)8
14. 𝑦=2+𝑥
( )
2−𝑥5
15. 𝑦=(2𝑥+ 5)−6
16. 𝑦= sin(sec 𝑥)
17. 𝑦=7
√𝑥4+3
18. 𝑦= 6cos8𝑥
19. 𝑦= cos2(𝑥7)
20. 𝑦=(𝑥3+ 4𝑥+ 5)−6
21. 𝑦=2000
sin 3𝑥
( )
22. 𝑦= sec ( 3x)
23.
y =(sin(𝑥))5
24. y = sin (𝑥5)
Section 2.6 Implicit Differentiation
25.
2𝑥𝑦 +𝑦10 = 11
26. 𝑥𝑦3+ 10𝑦11 = 9
27. 𝑦= sin (2𝑥𝑦)
28. 3x = y +(2𝑥−𝑦)2
29. 2cosy = 7𝑥sin 𝑦+ 7sin (2𝑦)
30.
5cos(𝑦)/sin = 1
(𝑥)
MAT 265 Mastery Exam Review NO CALCULATORS Page 3 of 5
Section 3.3 Derivatives of Exponential and Logarithmic Functions
31. 𝑦=𝑥5𝑒2𝑥
32. y = 𝑥6√𝑥+2
( )( )
𝑥+7 𝑥+5 6
33. 𝑦= ln((𝑥6+ 2𝑥)4)
34. 𝑦= ln(√(𝑥+ 6)(𝑥+ 7)(𝑥9+ 10)
8
35.
𝑦= 11csc𝑥
36. 𝑦=𝑥√𝑥
8
37 100
. 𝑦=𝑥6+𝑒10𝑥+𝑒4
38. 𝑦= 4𝑥tan𝑥
39. 𝑦= [𝑥ln 11(𝑥+ 12)13(𝑥8+ 9)10]
40. 𝑦=sec9(2𝑥)
Section 3.5 Inverse Trigonometric Functions
41. 𝑦= arccos(𝑥4)
42. 𝑦=tan−1 (2
𝑥3)
43. 𝑦= arcsin(𝑒𝑥)
44. 𝑦= arccos
(2 + 𝑥)
45.
𝑦= 9𝑥arcsin(𝑥)
MAT 265 Mastery Exam Review NO CALCULATORS Page 4 of 5
ANSWERS
1. 𝑦′ = 7 cos 𝑥+ 12(sec 𝑥)2− 3𝑥2
2. 𝑦′= 6.5𝑥5.5 +7.5
𝑥8.5
3. 𝑦′= 0
4. 𝑦′=√7 + √5
2√𝑥
5. 𝑦′= − 8
𝑥2−820
𝑥3
6. 𝑦′=9𝑥
54
4+ 5𝑥
3
2
7. 𝑦′= sec2(𝑥) + 11csc 𝑥 cot 𝑥
8. 𝑦′= − sin 𝑥 − csc2𝑥
9. 𝑦′= − sin(𝑥)
10. 𝑦′=11
2√𝑥(𝑥+6)
√2
11. 𝑦′=𝑥sec2(𝑥)−tan(𝑥) (𝑥tan(𝑥)+1)
6x2sec(𝑥)
12. 𝑦′=− cot 𝑥 csc 𝑥 (4+𝑥5)−5𝑥csc 𝑥
4
(4+𝑥)
5 2
13. 𝑦′= 15(3𝑥+ 4)4(6𝑥+ 7)8+ 48(3𝑥+ 4 6𝑥+ 7
)5( )7
14. 𝑦′ = 4(3+𝑥)
( )
2−𝑥6
15. 𝑦′= − 12
(2𝑥+5)7
16. 𝑦′= cos(sec 𝑥) ∙ sec 𝑥tan 𝑥
17. 𝑦′= − 14𝑥3
(𝑥+3)
4 1.5
18. 𝑦′= −48(cos 𝑥)7sin 𝑥
19. 𝑦′= −14𝑥 𝑥
6cos(7)sin(𝑥7)
20. 𝑦′=−6(3𝑥2+4)
(𝑥3+4𝑥+5)7
21. 𝑦′= − 6000 cos(3𝑥)
(sin 3𝑥)
( ) 2= −6000 csc 3𝑥3𝑥
( ) cot( )
22. 𝑦′ = 3 sec(3𝑥(3𝑥)
)tan 0
23. y′ = 5 (sin(𝑥))4cos(𝑥)
MAT 265 Mastery Exam Review NO CALCULATORS Page 5 of 5
24. y′ = 5𝑥4 cos (𝑥5)
25. 𝑦′= − 𝑦
𝑥+5𝑦9
26. 𝑦′= − 𝑦
3𝑥+110𝑦8
27. 𝑦′=2𝑦cos(2𝑥𝑦)
−2𝑥cos 2 +1
(𝑥𝑦)
28. 𝑦′=3−8𝑥+4𝑦
2𝑦+1−4𝑥
29. 𝑦′= − 7sin𝑦
7𝑥 𝑦+2 sin 𝑦+ (2𝑦)cos 14 cos
30. 𝑦′= − cos 𝑦cos 𝑥
sin𝑦sin𝑥
31. 𝑦′= (5 + 2𝑥)𝑥4𝑒2𝑥
32. y′ = 𝑥6√𝑥+2
( )( )
𝑥+7 𝑥+5 6(6
𝑥+1
2(𝑥+2) −1
𝑥+7 −6
𝑥+5)
33. 𝑦′=4(6𝑥5+2)
𝑥6+2𝑥
34. 𝑦′=1
8(1
𝑥+6 +1
𝑥+7 +9𝑥8
𝑥9+10)
35. 𝑦′= −11csc 𝑥∙ csc 𝑥cot 𝑥∙ ln (11)
36. 𝑦′=𝑥√𝑥
8 ( ln𝑥
8√𝑥7
8+1
√𝑥7
8)
37. 𝑦′= 600 10𝑥5+𝑒10𝑥
38. 𝑦′= 4𝑥tan 𝑥∙(tan 𝑥+𝑥sec2𝑥)ln 4
39. 𝑦′=11
𝑥+13
𝑥+12 +80𝑥7
𝑥8+9
40. 𝑦′=(9 ln 2 )2𝑥sec9(2𝑥)tan(2𝑥)
41. 𝑦′= − 4𝑥3
√1−𝑥8
42. 𝑦′= − 6𝑥2
𝑥6+4
43. 𝑦′=𝑒𝑥
√1−𝑒2𝑥
44. 𝑦′= − 1
√−𝑥2−4𝑥−3
45. 𝑦′= 9 (arcsin 𝑥+𝑥
√1−𝑥2)
