Derivatives worksheet with answers

Free printable Derivatives worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
xyx = 1

Let f(x) = 4x4 − 8x2 − 8x. Find the slope of the graph at x = 1, that is f′(1).

f(x) = 4x4 − 8x2 − 8xx = 1
f′(1) =
2.Easy
xyx = −1

Let f(x) = −3x3 + 9x2 + 4x + 8. Find the slope of the graph at x = −1, that is f′(−1).

f(x) = −3x3 + 9x2 + 4x + 8x = −1
f′(−1) =
3.Medium
xyx = 0.5

Let f(x) = x·e−0.5x. Find f′(0.5).

f(x) = x·e−0.5xx = 0.5
f′(0.5) =
4.Medium
xyx = 0.5

Let f(x) = x·e2x. Find f′(0.5).

f(x) = x·e2xx = 0.5
f′(0.5) =
5.Hard
xy

Let f(x) = x3 − 10.5x2 + 36x − 1. Find the x-coordinate x of the local minimum.

f(x) = x3 − 10.5x2 + 36x − 1
x =
6.Hard
xy

Let f(x) = x3 − 9x2 + 15x + 6. Find the x-coordinate x of the local maximum.

f(x) = x3 − 9x2 + 15x + 6
x =

Answer key

  1. 1. f′(1) = −8
  2. 2. f′(−1) = −23
  3. 3. f′(0.5) = 0.5841
  4. 4. f′(0.5) = 5.437
  5. 5. x = 4
  6. 6. x = 1

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