Instructor:
Chris King
Math 181
Derivative Skill Test Review
Find the first derivative of the following. Do not simplify.
1. f ( x ) = cos ( x ) sin ( x )
2x
2. f ( x ) = 5
x +1
3. f ( x ) = ( 3x + 7 x + 5 )
3
tan x
x3
5. f ( x ) =
x
2
⎛ 3 ⎞
6. f ( x ) = ⎜
⎝ x + 1 ⎟⎠
4
4. f ( x ) =
(
)(
7. f ( x ) = 6x 3 − 2x + 1 1− x 4
8. f ( x ) = sin x
)
⎛ x ⎞
9. f ( x ) = cos ⎜ 2
⎝ x + 2 ⎟⎠
10. f ( x ) = csc x
11. f ( x ) = 4x 3 cos ( x )
tan x
12. f ( x ) = 3
x + 16x − 5
13. f ( x ) = 3x12 x 2 − 7x
1
− sin x
14. f ( x ) =
3
(
)
15. f ( x ) = 4x 3 − 17x (16x − 8 )
15
1
⎛
⎞
16. f ( x ) = ⎜ x − 3 + sin x ⎟
⎝
⎠
x
(
6
17. f ( x ) = tan 2x 5 − 6x 4 + x 3
)
5
18. f ( x ) =
(
x7
19. f ( x ) = ( 2x 2 − x ) ( 6x 3 − x )
20. f ( x ) = sec x
(
21. f ( x ) = x10 ln e x + 3x 2
22. f ( x ) = ln ( 4 + cos x )
)
)
3
(
23. f ( x ) = ln cos 5 ( 3x 4 )
24. f ( x ) = e5 x
2
)
+7 x−13
25. f ( x ) = x 3etan x
(
26. f ( x ) = sin ( 3x + 5 )
4
)
x3 − 1
x2
28. f ( x ) = sec 7 ( 7e x )
27. f ( x ) =
29. f ( x ) = ln x −
1
ln x
1
cos x − 6x
3x − 1
31. f ( x ) =
5x + 19
4
6
32. f ( x ) = ( 3x − 4 ) ( 7x + 2 )
33. f ( x ) = sin ( 7x ) cos ( 9x )
30. f ( x ) =
34. f ( x ) = ( ln x )
35. f ( x ) =
(x
9
5
2
− 8x + 3)
5
36. f ( x ) = 3x cos x
37. f ( x ) = log 4 ( sec x )
x −1
38. f ( x ) = x
e
3
39. f ( x ) =
2x
x sin x
40. f ( x ) =
4
− x3
41. f ( x ) = e
42. f ( x ) = ln ( tan x )
43. f ( x ) = eπ
44. f ( x ) = 6 −3x csc x
(
45. f ( x ) = cot 4 x 3 sin ( 8x − 1)
)