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) = −4x5 + 3x2 − 9x + 2. Find the slope of the graph at x = −3, that is f′(−3).

f(x) = −4x5 + 3x2 − 9x + 2x = −3
f′(−3) =
2.Easy
xyx = 1

Let f(x) = −3x3 − 2x2 − 8x + 1. Find the slope of the graph at x = 1, that is f′(1).

f(x) = −3x3 − 2x2 − 8x + 1x = 1
f′(1) =
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 = 1

Let f(x) = ln(x2 + 4). Find f′(1).

f(x) = ln(x2 + 4)x = 1
f′(1) =
5.Hard
xy

Let f(x) = x3 − 9x2 + 24x − 6. Find the x-coordinate x of the local maximum.

f(x) = x3 − 9x2 + 24x − 6
x =
6.Hard
xy

Let f(x) = x3 − 1.5x2 − 6x + 4. Find the x-coordinate x of the local maximum.

f(x) = x3 − 1.5x2 − 6x + 4
x =

Answer key

  1. 1. f′(−3) = −1647
  2. 2. f′(1) = −21
  3. 3. f′(−1) = −0.6667
  4. 4. f′(1) = 0.4
  5. 5. x = 2
  6. 6. x = −1

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