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) = −x3 − 3x2 − 8x − 8. Find the slope of the graph at x = 3, that is f′(3).

f(x) = −x3 − 3x2 − 8x − 8x = 3
f′(3) =
2.Easy
xyx = −3

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

f(x) = 2x3 − 2x2 − x + 3x = −3
f′(−3) =
3.Medium
xyx = −1

Let f(x) = ln(2x2 + 5). Find f′(−1).

f(x) = ln(2x2 + 5)x = −1
f′(−1) =
4.Medium
xyx = 1.5

Let f(x) = x3·e0.5x. Find f′(1.5).

f(x) = x3·e0.5xx = 1.5
f′(1.5) =
5.Hard
xy

Let f(x) = x3 + 4.5x2 + 6x − 3. Find the x-coordinate x of the local minimum.

f(x) = x3 + 4.5x2 + 6x − 3
x =
6.Hard
xy

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

f(x) = x3 + 6x2 + 9x + 6
x =

Answer key

  1. 1. f′(3) = −53
  2. 2. f′(−3) = 65
  3. 3. f′(−1) = −0.5714
  4. 4. f′(1.5) = 17.86
  5. 5. x = −1
  6. 6. x = −1

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