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 = −2

Let f(x) = −5x5 + 3x2 − 1. Find the slope of the graph at x = −2, that is f′(−2).

f(x) = −5x5 + 3x2 − 1x = −2
f′(−2) =
2.Easy
xyx = −1

Let f(x) = 5x3 + 6x2 − 4x − 6. Find the slope of the graph at x = −1, that is f′(−1).

f(x) = 5x3 + 6x2 − 4x − 6x = −1
f′(−1) =
3.Medium
xyx = 1

Let f(x) = (3x − 1)4. Find f′(1).

f(x) = (3x − 1)4x = 1
f′(1) =
4.Medium
xyx = 2

Let f(x) = (4x − 1)3. Find f′(2).

f(x) = (4x − 1)3x = 2
f′(2) =
5.Hard
xy

Let f(x) = x3 + 10.5x2 + 36x + 4. Find the x-coordinate x of the local minimum.

f(x) = x3 + 10.5x2 + 36x + 4
x =
6.Hard
xy

Let f(x) = x3 − 1.5x2 − 6x − 4. Find the x-coordinate x of the local maximum.

f(x) = x3 − 1.5x2 − 6x − 4
x =

Answer key

  1. 1. f′(−2) = −412
  2. 2. f′(−1) = −1
  3. 3. f′(1) = 96
  4. 4. f′(2) = 588
  5. 5. x = −3
  6. 6. x = −1

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