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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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