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) = 5x4 + 3x2 − 7x + 9. Find the slope of the graph at x = −1, that is f′(−1).

f(x) = 5x4 + 3x2 − 7x + 9x = −1
f′(−1) =
2.Easy
xyx = −2

Let f(x) = 3x3 − 2x2 − 3x − 6. Find the slope of the graph at x = −2, that is f′(−2).

f(x) = 3x3 − 2x2 − 3x − 6x = −2
f′(−2) =
3.Medium
xyx = −2

Let f(x) = ln(3x2 + 4). Find f′(−2).

f(x) = ln(3x2 + 4)x = −2
f′(−2) =
4.Medium
xyx = 2

Let f(x) = x2·ex. Find f′(2).

f(x) = x2·exx = 2
f′(2) =
5.Hard
xy

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

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

Let f(x) = x3 − 4.5x2 + 6x. Find the x-coordinate x of the local maximum.

f(x) = x3 − 4.5x2 + 6x
x =

Answer key

  1. 1. f′(−1) = −33
  2. 2. f′(−2) = 41
  3. 3. f′(−2) = −0.75
  4. 4. f′(2) = 59.11
  5. 5. x = −4
  6. 6. x = 1

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