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) = 2x3 + x2 − 4x − 9. Find the slope of the graph at x = 2, that is f′(2).

f(x) = 2x3 + x2 − 4x − 9x = 2
f′(2) =
2.Easy
xyx = −1

Let f(x) = 2x5 − 4x2 − 7x − 1. Find the slope of the graph at x = −1, that is f′(−1).

f(x) = 2x5 − 4x2 − 7x − 1x = −1
f′(−1) =
3.Medium
xyx = 2

Let f(x) = ln(x2 + 2). Find f′(2).

f(x) = ln(x2 + 2)x = 2
f′(2) =
4.Medium
xyx = 0.5

Let f(x) = x2·e2x. Find f′(0.5).

f(x) = x2·e2xx = 0.5
f′(0.5) =
5.Hard
xyx = −1

The tangent line to f(x) = −x2 − 3x + 5 at x = −1 crosses the y-axis at y = b. Find b.

f(x) = −x2 − 3x + 5x = −1
b =
6.Hard
xy

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

f(x) = x3 + 10.5x2 + 36x + 4
x =

Answer key

  1. 1. f′(2) = 24
  2. 2. f′(−1) = 11
  3. 3. f′(2) = 0.6667
  4. 4. f′(0.5) = 4.077
  5. 5. b = 6
  6. 6. x = −4

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