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# Basic Rules of Differentiation Practice Questions

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Updated on Oct 1, 2011

To review these concepts, go to Basic Rules of Differentiation Study Guide.

## Basic Rules of Differentiation Practice Questions

Differentiate each of the following.

1. f(x)=x5
2. y = x7
3. g(u) = u–5
4. h(x) = 8
5. y = t4
6. y = x
7. f(x) = x100
8. f(t) = –11
9. h(x) = x
10. y = x
11. g(x) = x
12. k(x) = 4x
13. y = √u
14. y =
15. f(x) =
16. g(x) =

Differentiate the following.

1. y = 3x7
2. f(x) =
3. V(r) = π r3
4. g( t) =
5. k(x) = 1 – x2
6. y = 4t3 - 8t + 70
7. f(x) = 8x3 + 3x2
8. y = x2 – 3x + 5
9. s(t) = -16t2 + 5t + 200
10. F(x) = 6x100 + 10x50 – 4x25 + 2x10 – 9
11. g(x) = 3x + 5x3
12. h(u) = u5 + 4u4 – 7u3 – 2u2 + 8u – 2
13. y = 3 + +
14. y = u2u– 2
15. f(x) = 4x2 – 8x + 5 +
16. y = 4√x +
1. Find the first four derivatives of f(x) =
2. Find the second derivative of s(t) = –16t2 + 20t + 150.
3. Find the third derivative of y = 10x4 – 7x3 + 6x –1.
4. Find the first three derivatives of y =

### Solutions

1. f'(x) = 5x4
2. h'(x) = 0
3. f '(x) = 100x99
4. f '(t) = 0
5. h'(x) = 1·x0 = 1
6. k'(x) = –2x
7. f'(x) = 24x2 + 6x
8. s'(t) = –32t + 5
9. F'(x) = 600x99+ 500x49 – 100x24 + 20x9
10. h'(u) = 5u4 + 16u3 – 21u2 – 4u + 8
11. s"(t) = –32

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