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) = x4 + 9x2 + 9x + 3. Find the slope of the graph at x = 1, that is f′(1).

f(x) = x4 + 9x2 + 9x + 3x = 1
f′(1) =
2.Easy
xyx = 3

Let f(x) = −2x4 − 3x2 − 5x. Find the slope of the graph at x = 3, that is f′(3).

f(x) = −2x4 − 3x2 − 5xx = 3
f′(3) =
3.Medium
xyx = −1

Let f(x) = ln(2x2 + 1). Find f′(−1).

f(x) = ln(2x2 + 1)x = −1
f′(−1) =
4.Medium
xyx = 2

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

f(x) = x·sin(2x)x = 2 rad
f′(2) =
5.Hard
xy

Let f(x) = x3 + 10.5x2 + 36x + 3. Find the x-coordinate x of the local minimum.

f(x) = x3 + 10.5x2 + 36x + 3
x =
6.Hard
xy

Let f(x) = x3 + 3x2 + 1. Find the x-coordinate x of the local maximum.

f(x) = x3 + 3x2 + 1
x =

Answer key

  1. 1. f′(1) = 31
  2. 2. f′(3) = −239
  3. 3. f′(−1) = −1.333
  4. 4. f′(2) = −3.371
  5. 5. x = −3
  6. 6. x = −2

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