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) = −4x5 + 5x2 + 8x − 3. Find the slope of the graph at x = 1, that is f′(1).

f(x) = −4x5 + 5x2 + 8x − 3x = 1
f′(1) =
2.Easy
xyx = −1

Let f(x) = −2x3 + 6x2 + 5x + 7. Find the slope of the graph at x = −1, that is f′(−1).

f(x) = −2x3 + 6x2 + 5x + 7x = −1
f′(−1) =
3.Medium
xyx = 0.5

Let f(x) = x3·e−x. Find f′(0.5).

f(x) = x3·e−xx = 0.5
f′(0.5) =
4.Medium
xyx = 2

Let f(x) = (3x − 3)4. Find f′(2).

f(x) = (3x − 3)4x = 2
f′(2) =
5.Hard
xy

Let f(x) = x3 − 3x + 2. Find the x-coordinate x of the local maximum.

f(x) = x3 − 3x + 2
x =
6.Hard
xyx = −2

The tangent line to f(x) = 0.5x2 − 5x − 6 at x = −2 crosses the y-axis at y = b. Find b.

f(x) = 0.5x2 − 5x − 6x = −2
b =

Answer key

  1. 1. f′(1) = −2
  2. 2. f′(−1) = −13
  3. 3. f′(0.5) = 0.3791
  4. 4. f′(2) = 324
  5. 5. x = −1
  6. 6. b = −8

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