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

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

Let f(x) = −x5 + 8x2 − 6x + 3. Find the slope of the graph at x = −1, that is f′(−1).

f(x) = −x5 + 8x2 − 6x + 3x = −1
f′(−1) =
3.Medium
xyx = 2

Let f(x) = (3x − 3)5. Find f′(2).

f(x) = (3x − 3)5x = 2
f′(2) =
4.Medium
xyx = 1.5

Let f(x) = x3·e−x. Find f′(1.5).

f(x) = x3·e−xx = 1.5
f′(1.5) =
5.Hard
xy

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

f(x) = x3 + 9x2 + 24x
x =
6.Hard
xy

Let f(x) = x3 − 1.5x2 − 6x − 1. Find the x-coordinate x of the local maximum.

f(x) = x3 − 1.5x2 − 6x − 1
x =

Answer key

  1. 1. f′(−1) = −28
  2. 2. f′(−1) = −27
  3. 3. f′(2) = 1215
  4. 4. f′(1.5) = 0.7531
  5. 5. x = −4
  6. 6. x = −1

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