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) = 5x5 + 9x2 − 6x + 4. Find the slope of the graph at x = −1, that is f′(−1).

f(x) = 5x5 + 9x2 − 6x + 4x = −1
f′(−1) =
2.Easy
xyx = 2

Let f(x) = 4x4 + 2x2 + 3x + 9. Find the slope of the graph at x = 2, that is f′(2).

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

Let f(x) = ln(x2 + 1). Find f′(3).

f(x) = ln(x2 + 1)x = 3
f′(3) =
4.Medium
xyx = 0

Let f(x) = (2x + 5)5. Find f′(0).

f(x) = (2x + 5)5x = 0
f′(0) =
5.Hard
xyx = 1

The tangent line to f(x) = x2 − 2x − 5 at x = 1 crosses the y-axis at y = b. Find b.

f(x) = x2 − 2x − 5x = 1
b =
6.Hard
xy

Let f(x) = x3 + 3x2 − 9x + 5. Find the x-coordinate x of the local maximum.

f(x) = x3 + 3x2 − 9x + 5
x =

Answer key

  1. 1. f′(−1) = 1
  2. 2. f′(2) = 139
  3. 3. f′(3) = 0.6
  4. 4. f′(0) = 6250
  5. 5. b = −6
  6. 6. x = −3

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