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) = 2x5 − 2x2 − 5x + 7. Find the slope of the graph at x = −1, that is f′(−1).

f(x) = 2x5 − 2x2 − 5x + 7x = −1
f′(−1) =
2.Easy
xyx = −1

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

f(x) = −x5 + 8x2 − xx = −1
f′(−1) =
3.Medium
xyx = 0

Let f(x) = (4x − 3)4. Find f′(0).

f(x) = (4x − 3)4x = 0
f′(0) =
4.Medium
xyx = 0.5

Let f(x) = x2·e−0.5x. Find f′(0.5).

f(x) = x2·e−0.5xx = 0.5
f′(0.5) =
5.Hard
xyx = −2

The tangent line to f(x) = 2x2 + 5x + 5 at x = −2 crosses the y-axis at y = b. Find b.

f(x) = 2x2 + 5x + 5x = −2
b =
6.Hard
xy

Let f(x) = x3 − 7.5x2 + 18x + 3. Find the x-coordinate x of the local minimum.

f(x) = x3 − 7.5x2 + 18x + 3
x =

Answer key

  1. 1. f′(−1) = 9
  2. 2. f′(−1) = −22
  3. 3. f′(0) = −432
  4. 4. f′(0.5) = 0.6815
  5. 5. b = −3
  6. 6. x = 3

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