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 − 7x − 2. Find the slope of the graph at x = 1, that is f′(1).

f(x) = x4 + 9x2 − 7x − 2x = 1
f′(1) =
2.Easy
xyx = −3

Let f(x) = −5x5 + 5x2 + x + 4. Find the slope of the graph at x = −3, that is f′(−3).

f(x) = −5x5 + 5x2 + x + 4x = −3
f′(−3) =
3.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) =
4.Medium
xyx = −1

Let f(x) = ln(2x2 + 2). Find f′(−1).

f(x) = ln(2x2 + 2)x = −1
f′(−1) =
5.Hard
xy

Let f(x) = x3 − 9x2 + 15x − 5. Find the x-coordinate x of the local maximum.

f(x) = x3 − 9x2 + 15x − 5
x =
6.Hard
xy

Let f(x) = x3 + 3x2 − 9x − 2. Find the x-coordinate x of the local minimum.

f(x) = x3 + 3x2 − 9x − 2
x =

Answer key

  1. 1. f′(1) = 15
  2. 2. f′(−3) = −2054
  3. 3. f′(1.5) = −1.926
  4. 4. f′(−1) = −1
  5. 5. x = 1
  6. 6. x = 1

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