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

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

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

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

Let f(x) = x3·e2x. Find f′(2).

f(x) = x3·e2xx = 2
f′(2) =
4.Medium
xyx = 0

Let f(x) = (2x − 3)3. Find f′(0).

f(x) = (2x − 3)3x = 0
f′(0) =
5.Hard
xyx = −2

The tangent line to f(x) = x2 + 5x + 1 at x = −2 crosses the y-axis at y = b. Find b.

f(x) = x2 + 5x + 1x = −2
b =
6.Hard
xyx = −1

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

f(x) = 3x2 − x − 5x = −1
b =

Answer key

  1. 1. f′(−3) = 61
  2. 2. f′(−3) = −71
  3. 3. f′(2) = 1529
  4. 4. f′(0) = 54
  5. 5. b = −3
  6. 6. b = −8

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