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) = 3x3 − 5x2 + 4x − 6. Find the slope of the graph at x = −1, that is f′(−1).

f(x) = 3x3 − 5x2 + 4x − 6x = −1
f′(−1) =
2.Easy
xyx = 1

Let f(x) = −5x3 − 3x2 − 9x − 3. Find the slope of the graph at x = 1, that is f′(1).

f(x) = −5x3 − 3x2 − 9x − 3x = 1
f′(1) =
3.Medium
xyx = 0.5

Let f(x) = x2·ex. Find f′(0.5).

f(x) = x2·exx = 0.5
f′(0.5) =
4.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) =
5.Hard
xy

Let f(x) = x3 + 3x2 − 9x − 5. Find the x-coordinate x of the local maximum.

f(x) = x3 + 3x2 − 9x − 5
x =
6.Hard
xy

Let f(x) = x3 − 1.5x2 − 6x − 3. Find the x-coordinate x of the local minimum.

f(x) = x3 − 1.5x2 − 6x − 3
x =

Answer key

  1. 1. f′(−1) = 23
  2. 2. f′(1) = −30
  3. 3. f′(0.5) = 2.061
  4. 4. f′(2) = 5.482
  5. 5. x = −3
  6. 6. x = 2

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