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 = −3

Let f(x) = 2x5 − 3x2 − 3x + 2. Find the slope of the graph at x = −3, that is f′(−3).

f(x) = 2x5 − 3x2 − 3x + 2x = −3
f′(−3) =
2.Easy
xyx = −1

Let f(x) = 4x4 − x2 + 6x + 9. Find the slope of the graph at x = −1, that is f′(−1).

f(x) = 4x4 − x2 + 6x + 9x = −1
f′(−1) =
3.Medium
xyx = −2

Let f(x) = ln(x2 + 1). Find f′(−2).

f(x) = ln(x2 + 1)x = −2
f′(−2) =
4.Medium
xyx = 0

Let f(x) = (4x + 1)4. Find f′(0).

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

The tangent line to f(x) = 2x2 − 4x + 1 at x = −1 crosses the y-axis at y = b. Find b.

f(x) = 2x2 − 4x + 1x = −1
b =
6.Hard
xy

Let f(x) = x3 − 9x2 + 15x + 3. Find the x-coordinate x of the local maximum.

f(x) = x3 − 9x2 + 15x + 3
x =

Answer key

  1. 1. f′(−3) = 825
  2. 2. f′(−1) = −8
  3. 3. f′(−2) = −0.8
  4. 4. f′(0) = 16
  5. 5. b = −1
  6. 6. x = 1

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