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 − 3x2 + 4x − 1. Find the slope of the graph at x = 3, that is f′(3).

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

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

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

Let f(x) = ln(x2 + 2). Find f′(3).

f(x) = ln(x2 + 2)x = 3
f′(3) =
4.Medium
xyx = 2

Let f(x) = ln(x2 + 1). Find f′(2).

f(x) = ln(x2 + 1)x = 2
f′(2) =
5.Hard
xy

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

f(x) = x3 − 4.5x2 − 6
x =
6.Hard
xy

Let f(x) = x3 + 6x2 + 9x − 1. Find the x-coordinate x of the local minimum.

f(x) = x3 + 6x2 + 9x − 1
x =

Answer key

  1. 1. f′(3) = −230
  2. 2. f′(1) = −4
  3. 3. f′(3) = 0.5455
  4. 4. f′(2) = 0.8
  5. 5. x = 3
  6. 6. x = −1

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