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) = −2x3 − 5x2 − 7x − 1. Find the slope of the graph at x = −3, that is f′(−3).

f(x) = −2x3 − 5x2 − 7x − 1x = −3
f′(−3) =
2.Easy
xyx = −3

Let f(x) = −4x5 + 5x2 + 3x + 8. Find the slope of the graph at x = −3, that is f′(−3).

f(x) = −4x5 + 5x2 + 3x + 8x = −3
f′(−3) =
3.Medium
xyx = 1

Let f(x) = x3·e0.5x. Find f′(1).

f(x) = x3·e0.5xx = 1
f′(1) =
4.Medium
xyx = 3

Let f(x) = ln(2x2 + 2). Find f′(3).

f(x) = ln(2x2 + 2)x = 3
f′(3) =
5.Hard
xy

Let f(x) = x3 − 13.5x2 + 54x + 5. Find the x-coordinate x of the local maximum.

f(x) = x3 − 13.5x2 + 54x + 5
x =
6.Hard
xy

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

f(x) = x3 + 1.5x2 − 6x − 6
x =

Answer key

  1. 1. f′(−3) = −31
  2. 2. f′(−3) = −1647
  3. 3. f′(1) = 5.771
  4. 4. f′(3) = 0.6
  5. 5. x = 3
  6. 6. x = −2

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