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) = 3x5 − x2 + x − 8. Find the slope of the graph at x = −2, that is f′(−2).

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

Let f(x) = 2x5 + 5x2 − 5x − 5. Find the slope of the graph at x = 3, that is f′(3).

f(x) = 2x5 + 5x2 − 5x − 5x = 3
f′(3) =
3.Medium
xyx = 2

Let f(x) = (−2x + 3)3. Find f′(2).

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

Let f(x) = (2x − 3)4. Find f′(2).

f(x) = (2x − 3)4x = 2
f′(2) =
5.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 =
6.Hard
xy

Let f(x) = x3 + 7.5x2 + 18x + 6. Find the x-coordinate x of the local maximum.

f(x) = x3 + 7.5x2 + 18x + 6
x =

Answer key

  1. 1. f′(−2) = 245
  2. 2. f′(3) = 835
  3. 3. f′(2) = −6
  4. 4. f′(2) = 8
  5. 5. x = −3
  6. 6. x = −3

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