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 = 3

Let f(x) = −5x5 − 7x2 − 9x − 5. Find the slope of the graph at x = 3, that is f′(3).

f(x) = −5x5 − 7x2 − 9x − 5x = 3
f′(3) =
2.Easy
xyx = −2

Let f(x) = 3x5 − 6x2 + 4x + 6. Find the slope of the graph at x = −2, that is f′(−2).

f(x) = 3x5 − 6x2 + 4x + 6x = −2
f′(−2) =
3.Medium
xyx = −1

Let f(x) = ln(x2 + 1). Find f′(−1).

f(x) = ln(x2 + 1)x = −1
f′(−1) =
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 + 7.5x2 + 12x − 2. Find the x-coordinate x of the local minimum.

f(x) = x3 + 7.5x2 + 12x − 2
x =
6.Hard
xy

Let f(x) = x3 − 3x2 − 9x + 2. Find the x-coordinate x of the local maximum.

f(x) = x3 − 3x2 − 9x + 2
x =

Answer key

  1. 1. f′(3) = −2076
  2. 2. f′(−2) = 268
  3. 3. f′(−1) = −1
  4. 4. f′(0.5) = 0.3033
  5. 5. x = −1
  6. 6. x = −1

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