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) = 2x5 + 5x2 − 9x − 7. Find the slope of the graph at x = −1, that is f′(−1).

f(x) = 2x5 + 5x2 − 9x − 7x = −1
f′(−1) =
2.Easy
xyx = 2

Let f(x) = 3x3 − 4x2 − 7x. Find the slope of the graph at x = 2, that is f′(2).

f(x) = 3x3 − 4x2 − 7xx = 2
f′(2) =
3.Medium
xyx = 0.5

Let f(x) = x2·e−0.5x. Find f′(0.5).

f(x) = x2·e−0.5xx = 0.5
f′(0.5) =
4.Medium
xyx = 0

Let f(x) = (−2x + 5)5. Find f′(0).

f(x) = (−2x + 5)5x = 0
f′(0) =
5.Hard
xy

Let f(x) = x3 − 3x + 6. Find the x-coordinate x of the local maximum.

f(x) = x3 − 3x + 6
x =
6.Hard
xy

Let f(x) = x3 − 9x2 + 24x + 6. Find the x-coordinate x of the local maximum.

f(x) = x3 − 9x2 + 24x + 6
x =

Answer key

  1. 1. f′(−1) = −9
  2. 2. f′(2) = 13
  3. 3. f′(0.5) = 0.6815
  4. 4. f′(0) = −6250
  5. 5. x = −1
  6. 6. x = 2

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