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) = −x5 − 7x2 + 2x − 7. Find the slope of the graph at x = −3, that is f′(−3).

f(x) = −x5 − 7x2 + 2x − 7x = −3
f′(−3) =
2.Easy
xyx = 3

Let f(x) = x3 − 2x2 + 9x − 7. Find the slope of the graph at x = 3, that is f′(3).

f(x) = x3 − 2x2 + 9x − 7x = 3
f′(3) =
3.Medium
xyx = 0

Let f(x) = (2x − 1)4. Find f′(0).

f(x) = (2x − 1)4x = 0
f′(0) =
4.Medium
xyx = 2

Let f(x) = (3x + 1)3. Find f′(2).

f(x) = (3x + 1)3x = 2
f′(2) =
5.Hard
xy

Let f(x) = x3 − 9x2 + 15x + 5. Find the x-coordinate x of the local minimum.

f(x) = x3 − 9x2 + 15x + 5
x =
6.Hard
xy

Let f(x) = x3 − 13.5x2 + 54x − 4. Find the x-coordinate x of the local maximum.

f(x) = x3 − 13.5x2 + 54x − 4
x =

Answer key

  1. 1. f′(−3) = −361
  2. 2. f′(3) = 24
  3. 3. f′(0) = −8
  4. 4. f′(2) = 441
  5. 5. x = 5
  6. 6. x = 3

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