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 + 4x2 − 5x − 1. Find the slope of the graph at x = −1, that is f′(−1).

f(x) = x4 + 4x2 − 5x − 1x = −1
f′(−1) =
2.Easy
xyx = −1

Let f(x) = −x3 + 2x2 + 3x − 7. Find the slope of the graph at x = −1, that is f′(−1).

f(x) = −x3 + 2x2 + 3x − 7x = −1
f′(−1) =
3.Medium
xyx = 2

Let f(x) = ln(3x2 + 2). Find f′(2).

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

Let f(x) = (−2x + 1)4. Find f′(2).

f(x) = (−2x + 1)4x = 2
f′(2) =
5.Hard
xy

Let f(x) = x3 − 9x2 + 15x + 2. Find the x-coordinate x of the local minimum.

f(x) = x3 − 9x2 + 15x + 2
x =
6.Hard
xy

Let f(x) = x3 + 3x2 − 9x − 6. Find the x-coordinate x of the local minimum.

f(x) = x3 + 3x2 − 9x − 6
x =

Answer key

  1. 1. f′(−1) = −17
  2. 2. f′(−1) = −4
  3. 3. f′(2) = 0.8571
  4. 4. f′(2) = 216
  5. 5. x = 5
  6. 6. x = 1

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