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) = 4x3 − 2x2 + 7x + 4. Find the slope of the graph at x = 1, that is f′(1).

f(x) = 4x3 − 2x2 + 7x + 4x = 1
f′(1) =
2.Easy
xyx = −3

Let f(x) = 5x3 − 7x2 + 9x + 7. Find the slope of the graph at x = −3, that is f′(−3).

f(x) = 5x3 − 7x2 + 9x + 7x = −3
f′(−3) =
3.Medium
xyx = 2

Let f(x) = x2·e2x. Find f′(2).

f(x) = x2·e2xx = 2
f′(2) =
4.Medium
xyx = −1

Let f(x) = (2x − 3)3. Find f′(−1).

f(x) = (2x − 3)3x = −1
f′(−1) =
5.Hard
xyx = 1

The tangent line to f(x) = x2 − 2x − 3 at x = 1 crosses the y-axis at y = b. Find b.

f(x) = x2 − 2x − 3x = 1
b =
6.Hard
xy

Let f(x) = x3 + 7.5x2 + 18x + 1. Find the x-coordinate x of the local maximum.

f(x) = x3 + 7.5x2 + 18x + 1
x =

Answer key

  1. 1. f′(1) = 15
  2. 2. f′(−3) = 186
  3. 3. f′(2) = 655.2
  4. 4. f′(−1) = 150
  5. 5. b = −4
  6. 6. x = −3

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