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

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

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

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

Let f(x) = ln(3x2 + 2). Find f′(3).

f(x) = ln(3x2 + 2)x = 3
f′(3) =
4.Medium
xyx = 1.5

Let f(x) = x·sin(3x), with x in radians. Find f′(1.5).

f(x) = x·sin(3x)x = 1.5 rad
f′(1.5) =
5.Hard
xy

Let f(x) = x3 − 9x2 + 24x − 3. Find the x-coordinate x of the local minimum.

f(x) = x3 − 9x2 + 24x − 3
x =
6.Hard
xy

Let f(x) = x3 − 12x2 + 36x − 1. Find the x-coordinate x of the local minimum.

f(x) = x3 − 12x2 + 36x − 1
x =

Answer key

  1. 1. f′(−1) = 15
  2. 2. f′(−2) = −3
  3. 3. f′(3) = 0.6207
  4. 4. f′(1.5) = −1.926
  5. 5. x = 4
  6. 6. x = 6

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