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) = −3x4 − 4x2 + 5x − 7. Find the slope of the graph at x = −3, that is f′(−3).

f(x) = −3x4 − 4x2 + 5x − 7x = −3
f′(−3) =
2.Easy
xyx = 1

Let f(x) = −2x3 + 9x2 + 9x + 6. Find the slope of the graph at x = 1, that is f′(1).

f(x) = −2x3 + 9x2 + 9x + 6x = 1
f′(1) =
3.Medium
xyx = 2

Let f(x) = x·sin(3x), with x in radians. Find f′(2).

f(x) = x·sin(3x)x = 2 rad
f′(2) =
4.Medium
xyx = −1

Let f(x) = (2x + 3)3. Find f′(−1).

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

Let f(x) = x3 − 6x2 + 2. Find the x-coordinate x of the local minimum.

f(x) = x3 − 6x2 + 2
x =
6.Hard
xy

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

f(x) = x3 − 4.5x2 + 3
x =

Answer key

  1. 1. f′(−3) = 353
  2. 2. f′(1) = 21
  3. 3. f′(2) = 5.482
  4. 4. f′(−1) = 6
  5. 5. x = 4
  6. 6. x = 3

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