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

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

Let f(x) = −4x4 − 9x2 − 9x − 8. Find the slope of the graph at x = −1, that is f′(−1).

f(x) = −4x4 − 9x2 − 9x − 8x = −1
f′(−1) =
3.Medium
xyx = −1

Let f(x) = (2x + 5)4. Find f′(−1).

f(x) = (2x + 5)4x = −1
f′(−1) =
4.Medium
xyx = 1.5

Let f(x) = x3·e0.5x. Find f′(1.5).

f(x) = x3·e0.5xx = 1.5
f′(1.5) =
5.Hard
xy

Let f(x) = x3 + 4.5x2 + 6x − 2. Find the x-coordinate x of the local maximum.

f(x) = x3 + 4.5x2 + 6x − 2
x =
6.Hard
xyx = −2

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

f(x) = 0.5x2 + 2xx = −2
b =

Answer key

  1. 1. f′(3) = 47
  2. 2. f′(−1) = 25
  3. 3. f′(−1) = 216
  4. 4. f′(1.5) = 17.86
  5. 5. x = −2
  6. 6. b = −2

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