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 = −3

Let f(x) = −x5 + x2 + 8x − 7. Find the slope of the graph at x = −3, that is f′(−3).

f(x) = −x5 + x2 + 8x − 7x = −3
f′(−3) =
2.Easy
xyx = 1

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

f(x) = −2x5 − 2x2 − x − 7x = 1
f′(1) =
3.Medium
xyx = 1.5

Let f(x) = x·ex. Find f′(1.5).

f(x) = x·exx = 1.5
f′(1.5) =
4.Medium
xyx = 2

Let f(x) = (−2x − 3)4. Find f′(2).

f(x) = (−2x − 3)4x = 2
f′(2) =
5.Hard
xy

Let f(x) = x3 + 1.5x2 − 6x + 2. Find the x-coordinate x of the local maximum.

f(x) = x3 + 1.5x2 − 6x + 2
x =
6.Hard
xy

Let f(x) = x3 − 9x2 + 24x − 5. Find the x-coordinate x of the local minimum.

f(x) = x3 − 9x2 + 24x − 5
x =

Answer key

  1. 1. f′(−3) = −403
  2. 2. f′(1) = −15
  3. 3. f′(1.5) = 11.2
  4. 4. f′(2) = 2744
  5. 5. x = −2
  6. 6. x = 4

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