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) = −3x3 + 7x2 − 7x + 1. Find the slope of the graph at x = −2, that is f′(−2).

f(x) = −3x3 + 7x2 − 7x + 1x = −2
f′(−2) =
2.Easy
xyx = −1

Let f(x) = −2x4 − 4x2 + 7x + 7. Find the slope of the graph at x = −1, that is f′(−1).

f(x) = −2x4 − 4x2 + 7x + 7x = −1
f′(−1) =
3.Medium
xyx = 0.5

Let f(x) = x3·ex. Find f′(0.5).

f(x) = x3·exx = 0.5
f′(0.5) =
4.Medium
xyx = 1.5

Let f(x) = x·sin(2x), with x in radians. Find f′(1.5).

f(x) = x·sin(2x)x = 1.5 rad
f′(1.5) =
5.Hard
xyx = 3

The tangent line to f(x) = 0.5x2 − 2x − 5 at x = 3 crosses the y-axis at y = b. Find b.

f(x) = 0.5x2 − 2x − 5x = 3
b =
6.Hard
xy

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

f(x) = x3 − 3x2 − 2
x =

Answer key

  1. 1. f′(−2) = −71
  2. 2. f′(−1) = 23
  3. 3. f′(0.5) = 1.443
  4. 4. f′(1.5) = −2.829
  5. 5. b = −9.5
  6. 6. x = 2

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