calculus 1
aknown11
MATH 2413-03
Derivative Worksheet
NAME:
DATE:
Solve each problem to match it to the corresponding word. Work must be shown on an attached (STAPLED) page.
1. Find dy
dx for x2 + y2 = 1 at (0, 1) 2y/x2 but
2. Find dy
dx for ex/y = x−y
−1 √
1 −x2 training
3. Find dy
dx for y = cos(x3) (ln(x))2 + 2 ln(x) life
4. Find dy
dx for y = x3 cos(x)
y −ex/y
y −ex/yx/y of
5. Find an equation for the tangent line 3
√ 1 − 9x2
the
to the curve ey + xy = e at (0, 1)
6. Find dy
dx for tan(x + 2y) − sin(x) = 1 3 csc(3x) sec(3x) live
at (
0, π
8
) 7. Find
d2y
d2x for xy + x3 = 4 1 and
8. Find dy
dx for xy2 −x2y − 2 = 0 at (1,−1)
1
x ln(x) minute
9. Find f ′(x) for f(x) = sin−1(3x) 3x2 cos(x) −x3 sin(x) now
10. Find g′(x) for g(x) = tan−1(x2) ln(x) + 1
x ln(x) rest
11. Find h′(x) −1 4
hated
for h(x) = sin−1(x) + 2 cos−1(x)
12. Find y′ for y = ln(ln(x)) 2x
1 + x4 Suffer
13. Find y′ for y = ln(x ln(x)) 0 champion
14. Find y′ for y = x(ln(x))2 −sin(x3)3x2 Don’t
15. Find y′ for y = ln(tan(3x)) y = −1 e x + 1 I
16. Find dy
dx for y = (x + 2)1/x (ln(x) + 1)xx said
17. Find y′ for y = xx (
ln(cos(x)) − x sin(x)
cos(x)
) cos(x)x as
18. Find y′′ for y = xx y(ln(x) + 1) of
19. Find h′(x) for h(x) = ( √
cos(x))x −2x(1 + y2) quit
20. Find y′ for y = cos(x)x cos(x) ln(cos(x)) −x sin(x)
2 cos(x) ( √
cos(x))x a
21. Find dy
dx for tan−1 (y) + x2 = 0 (x(ln(x) + 1)2 + 1)xx−1 your
22. Find dy
dx for ln(y) −x ln(x) = −1
( 1
x(x + 2) −
ln(x + 2)
x2
) (x + 2)1/x every
5 6 16 12 2 11,
7 5 17, ′
3 21. 10
4 8 15 9 13 2
18 14 20 19 1
-Muhammad Ali
2