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 = −2

Let f(x) = −x4 + x2 + 8x − 8. Find the slope of the graph at x = −2, that is f′(−2).

f(x) = −x4 + x2 + 8x − 8x = −2
f′(−2) =
2.Easy
xyx = −3

Let f(x) = −x4 − 5x2 − 7x − 4. Find the slope of the graph at x = −3, that is f′(−3).

f(x) = −x4 − 5x2 − 7x − 4x = −3
f′(−3) =
3.Medium
xyx = −1

Let f(x) = (3x + 1)5. Find f′(−1).

f(x) = (3x + 1)5x = −1
f′(−1) =
4.Medium
xyx = 0

Let f(x) = (4x + 1)3. Find f′(0).

f(x) = (4x + 1)3x = 0
f′(0) =
5.Hard
xy

Let f(x) = x3 − 9x2 + 24x − 2. Find the x-coordinate x of the local minimum.

f(x) = x3 − 9x2 + 24x − 2
x =
6.Hard
xyx = −1

The tangent line to f(x) = x2 − 5x + 5 at x = −1 crosses the y-axis at y = b. Find b.

f(x) = x2 − 5x + 5x = −1
b =

Answer key

  1. 1. f′(−2) = 36
  2. 2. f′(−3) = 131
  3. 3. f′(−1) = 240
  4. 4. f′(0) = 12
  5. 5. x = 4
  6. 6. b = 4

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