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) = −x3 + 4x2 − 2x + 6. Find the slope of the graph at x = −2, that is f′(−2).

f(x) = −x3 + 4x2 − 2x + 6x = −2
f′(−2) =
2.Easy
xyx = −1

Let f(x) = x4 + 2x2 − 6x − 9. Find the slope of the graph at x = −1, that is f′(−1).

f(x) = x4 + 2x2 − 6x − 9x = −1
f′(−1) =
3.Medium
xyx = 0.5

Let f(x) = x·ex. Find f′(0.5).

f(x) = x·exx = 0.5
f′(0.5) =
4.Medium
xyx = 1

Let f(x) = x3·e−0.5x. Find f′(1).

f(x) = x3·e−0.5xx = 1
f′(1) =
5.Hard
xy

Let f(x) = x3 − 10.5x2 + 30x. Find the x-coordinate x of the local minimum.

f(x) = x3 − 10.5x2 + 30x
x =
6.Hard
xy

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

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

Answer key

  1. 1. f′(−2) = −30
  2. 2. f′(−1) = −14
  3. 3. f′(0.5) = 2.473
  4. 4. f′(1) = 1.516
  5. 5. x = 5
  6. 6. x = −1

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