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

f(x) = −2x5 + 3x2 − 8x − 1x = 2
f′(2) =
2.Easy
xyx = −2

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

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

Let f(x) = (3x + 1)4. Find f′(1).

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

Let f(x) = x3·e−x. Find f′(1).

f(x) = x3·e−xx = 1
f′(1) =
5.Hard
xy

Let f(x) = x3 + 6x2 + 2. Find the x-coordinate x of the local maximum.

f(x) = x3 + 6x2 + 2
x =
6.Hard
xy

Let f(x) = x3 − 9x2 + 24x − 2. Find the x-coordinate x of the local maximum.

f(x) = x3 − 9x2 + 24x − 2
x =

Answer key

  1. 1. f′(2) = −156
  2. 2. f′(−2) = 161
  3. 3. f′(1) = 768
  4. 4. f′(1) = 0.7358
  5. 5. x = −4
  6. 6. x = 2

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