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 = −2

Let f(x) = −4x3 + 2x2 − 4x − 5. Find the slope of the graph at x = −2, that is f′(−2).

f(x) = −4x3 + 2x2 − 4x − 5x = −2
f′(−2) =
2.Easy
xyx = 2

Let f(x) = −5x3 − x2 + 4x − 1. Find the slope of the graph at x = 2, that is f′(2).

f(x) = −5x3 − x2 + 4x − 1x = 2
f′(2) =
3.Medium
xyx = 2

Let f(x) = ln(x2 + 2). Find f′(2).

f(x) = ln(x2 + 2)x = 2
f′(2) =
4.Medium
xyx = 0.5

Let f(x) = x·e−x. Find f′(0.5).

f(x) = x·e−xx = 0.5
f′(0.5) =
5.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 =
6.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 =

Answer key

  1. 1. f′(−2) = −60
  2. 2. f′(2) = −60
  3. 3. f′(2) = 0.6667
  4. 4. f′(0.5) = 0.3033
  5. 5. x = −1
  6. 6. b = 4

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