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 = 1

Let f(x) = −4x3 + 8x2 + 9. Find the slope of the graph at x = 1, that is f′(1).

f(x) = −4x3 + 8x2 + 9x = 1
f′(1) =
2.Easy
xyx = 3

Let f(x) = 4x4 − 8x2 − 5x + 1. Find the slope of the graph at x = 3, that is f′(3).

f(x) = 4x4 − 8x2 − 5x + 1x = 3
f′(3) =
3.Medium
xyx = 2

Let f(x) = x·e−x. Find f′(2).

f(x) = x·e−xx = 2
f′(2) =
4.Medium
xyx = 2

Let f(x) = (−2x + 1)5. Find f′(2).

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

Let f(x) = x3 + 3x2 − 9x. Find the x-coordinate x of the local minimum.

f(x) = x3 + 3x2 − 9x
x =
6.Hard
xy

Let f(x) = x3 − 6x2 + 9x + 3. Find the x-coordinate x of the local maximum.

f(x) = x3 − 6x2 + 9x + 3
x =

Answer key

  1. 1. f′(1) = 4
  2. 2. f′(3) = 379
  3. 3. f′(2) = −0.1353
  4. 4. f′(2) = −810
  5. 5. x = 1
  6. 6. x = 1

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