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 + 9x + 5. Find the slope of the graph at x = 2, that is f′(2).

f(x) = 3x5 − x2 + 9x + 5x = 2
f′(2) =
2.Easy
xyx = −2

Let f(x) = −4x3 + x2 − 7x − 4. Find the slope of the graph at x = −2, that is f′(−2).

f(x) = −4x3 + x2 − 7x − 4x = −2
f′(−2) =
3.Medium
xyx = 0.5

Let f(x) = x·sin(x), with x in radians. Find f′(0.5).

f(x) = x·sin(x)x = 0.5 rad
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 + 1.5x2 − 4. Find the x-coordinate x of the local maximum.

f(x) = x3 + 1.5x2 − 4
x =
6.Hard
xy

Let f(x) = x3 + 10.5x2 + 36x − 6. Find the x-coordinate x of the local minimum.

f(x) = x3 + 10.5x2 + 36x − 6
x =

Answer key

  1. 1. f′(2) = 245
  2. 2. f′(−2) = −59
  3. 3. f′(0.5) = 0.9182
  4. 4. f′(2) = 5.482
  5. 5. x = −1
  6. 6. x = −3

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