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 = −3

Let f(x) = 3x5 − 5x2 + 7x + 7. Find the slope of the graph at x = −3, that is f′(−3).

f(x) = 3x5 − 5x2 + 7x + 7x = −3
f′(−3) =
2.Easy
xyx = −1

Let f(x) = 3x5 − 4x2 − 1. Find the slope of the graph at x = −1, that is f′(−1).

f(x) = 3x5 − 4x2 − 1x = −1
f′(−1) =
3.Medium
xyx = 0.5

Let f(x) = x2·e0.5x. Find f′(0.5).

f(x) = x2·e0.5xx = 0.5
f′(0.5) =
4.Medium
xyx = 1.5

Let f(x) = x·e2x. Find f′(1.5).

f(x) = x·e2xx = 1.5
f′(1.5) =
5.Hard
xyx = −2

The tangent line to f(x) = 0.5x2 + 2x − 6 at x = −2 crosses the y-axis at y = b. Find b.

f(x) = 0.5x2 + 2x − 6x = −2
b =
6.Hard
xy

Let f(x) = x3 + 3x2 − 9x + 2. Find the x-coordinate x of the local maximum.

f(x) = x3 + 3x2 − 9x + 2
x =

Answer key

  1. 1. f′(−3) = 1252
  2. 2. f′(−1) = 23
  3. 3. f′(0.5) = 1.445
  4. 4. f′(1.5) = 80.34
  5. 5. b = −8
  6. 6. x = −3

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