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) = 5x4 − 6x2 + 4x + 5. Find the slope of the graph at x = −1, that is f′(−1).

f(x) = 5x4 − 6x2 + 4x + 5x = −1
f′(−1) =
2.Easy
xyx = 1

Let f(x) = 3x3 − 2x2 + 6x − 1. Find the slope of the graph at x = 1, that is f′(1).

f(x) = 3x3 − 2x2 + 6x − 1x = 1
f′(1) =
3.Medium
xyx = 0

Let f(x) = (3x + 5)3. Find f′(0).

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

Let f(x) = (4x + 5)5. Find f′(1).

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

The tangent line to f(x) = x2 + 4x + 3 at x = −1 crosses the y-axis at y = b. Find b.

f(x) = x2 + 4x + 3x = −1
b =
6.Hard
xy

Let f(x) = x3 + 6x2 + 9x + 2. Find the x-coordinate x of the local minimum.

f(x) = x3 + 6x2 + 9x + 2
x =

Answer key

  1. 1. f′(−1) = −4
  2. 2. f′(1) = 11
  3. 3. f′(0) = 225
  4. 4. f′(1) = 131220
  5. 5. b = 2
  6. 6. x = −1

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