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) = −2x5 + 8x2 − 4x − 4. Find the slope of the graph at x = 2, that is f′(2).

f(x) = −2x5 + 8x2 − 4x − 4x = 2
f′(2) =
2.Easy
xyx = 2

Let f(x) = 2x3 − 8x2 − x + 5. Find the slope of the graph at x = 2, that is f′(2).

f(x) = 2x3 − 8x2 − x + 5x = 2
f′(2) =
3.Medium
xyx = 1

Let f(x) = ln(x2 + 2). Find f′(1).

f(x) = ln(x2 + 2)x = 1
f′(1) =
4.Medium
xyx = 0

Let f(x) = (3x + 1)4. Find f′(0).

f(x) = (3x + 1)4x = 0
f′(0) =
5.Hard
xy

Let f(x) = x3 + 10.5x2 + 36x + 1. Find the x-coordinate x of the local minimum.

f(x) = x3 + 10.5x2 + 36x + 1
x =
6.Hard
xyx = 3

The tangent line to f(x) = 2x2 + 4x at x = 3 crosses the y-axis at y = b. Find b.

f(x) = 2x2 + 4xx = 3
b =

Answer key

  1. 1. f′(2) = −132
  2. 2. f′(2) = −9
  3. 3. f′(1) = 0.6667
  4. 4. f′(0) = 12
  5. 5. x = −3
  6. 6. b = −18

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