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 + 8x2 + 6x + 6. Find the slope of the graph at x = −3, that is f′(−3).

f(x) = −x3 + 8x2 + 6x + 6x = −3
f′(−3) =
2.Easy
xyx = 2

Let f(x) = −4x5 − 8x2 + 7x − 2. Find the slope of the graph at x = 2, that is f′(2).

f(x) = −4x5 − 8x2 + 7x − 2x = 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 = 1.5

Let f(x) = x·e0.5x. Find f′(1.5).

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

Let f(x) = x3 − 6x2 + 9x − 1. Find the x-coordinate x of the local maximum.

f(x) = x3 − 6x2 + 9x − 1
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′(−3) = −69
  2. 2. f′(2) = −345
  3. 3. f′(0.5) = 0.9182
  4. 4. f′(1.5) = 3.705
  5. 5. x = 1
  6. 6. x = −3

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