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) = −2x3 + 4x2 + 3x − 4. Find the slope of the graph at x = −1, that is f′(−1).

f(x) = −2x3 + 4x2 + 3x − 4x = −1
f′(−1) =
2.Easy
xyx = 1

Let f(x) = −4x4 − 5x2 − 8x − 5. Find the slope of the graph at x = 1, that is f′(1).

f(x) = −4x4 − 5x2 − 8x − 5x = 1
f′(1) =
3.Medium
xyx = 2

Let f(x) = ln(2x2 + 1). Find f′(2).

f(x) = ln(2x2 + 1)x = 2
f′(2) =
4.Medium
xyx = 1.5

Let f(x) = x2·e2x. Find f′(1.5).

f(x) = x2·e2xx = 1.5
f′(1.5) =
5.Hard
xy

Let f(x) = x3 + 10.5x2 + 36x − 1. Find the x-coordinate x of the local minimum.

f(x) = x3 + 10.5x2 + 36x − 1
x =
6.Hard
xy

Let f(x) = x3 + 4.5x2 + 6x + 4. Find the x-coordinate x of the local maximum.

f(x) = x3 + 4.5x2 + 6x + 4
x =

Answer key

  1. 1. f′(−1) = −11
  2. 2. f′(1) = −34
  3. 3. f′(2) = 0.8889
  4. 4. f′(1.5) = 150.6
  5. 5. x = −3
  6. 6. x = −2

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