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) = 2x4 − 6x2 − 8x + 8. Find the slope of the graph at x = −3, that is f′(−3).

f(x) = 2x4 − 6x2 − 8x + 8x = −3
f′(−3) =
2.Easy
xyx = −2

Let f(x) = −3x5 − x2 − 2x − 3. Find the slope of the graph at x = −2, that is f′(−2).

f(x) = −3x5 − x2 − 2x − 3x = −2
f′(−2) =
3.Medium
xyx = 0

Let f(x) = (−2x + 1)3. Find f′(0).

f(x) = (−2x + 1)3x = 0
f′(0) =
4.Medium
xyx = 3

Let f(x) = ln(x2 + 1). Find f′(3).

f(x) = ln(x2 + 1)x = 3
f′(3) =
5.Hard
xy

Let f(x) = x3 − 12x2 + 36x + 5. Find the x-coordinate x of the local maximum.

f(x) = x3 − 12x2 + 36x + 5
x =
6.Hard
xyx = −1

The tangent line to f(x) = 3x2 + 2 at x = −1 crosses the y-axis at y = b. Find b.

f(x) = 3x2 + 2x = −1
b =

Answer key

  1. 1. f′(−3) = −188
  2. 2. f′(−2) = −238
  3. 3. f′(0) = −6
  4. 4. f′(3) = 0.6
  5. 5. x = 2
  6. 6. b = −1

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