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) = −3x5 − 8x2 − 9x + 2. Find the slope of the graph at x = −2, that is f′(−2).

f(x) = −3x5 − 8x2 − 9x + 2x = −2
f′(−2) =
2.Easy
xyx = 3

Let f(x) = 3x5 + 7x2 + 6x − 5. Find the slope of the graph at x = 3, that is f′(3).

f(x) = 3x5 + 7x2 + 6x − 5x = 3
f′(3) =
3.Medium
xyx = 2

Let f(x) = x2·ex. Find f′(2).

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

Let f(x) = ln(x2 + 4). Find f′(−1).

f(x) = ln(x2 + 4)x = −1
f′(−1) =
5.Hard
xyx = 2

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

f(x) = x2 − 3x + 2x = 2
b =
6.Hard
xy

Let f(x) = x3 − 1.5x2 − 6x − 5. Find the x-coordinate x of the local minimum.

f(x) = x3 − 1.5x2 − 6x − 5
x =

Answer key

  1. 1. f′(−2) = −217
  2. 2. f′(3) = 1263
  3. 3. f′(2) = 59.11
  4. 4. f′(−1) = −0.4
  5. 5. b = −2
  6. 6. x = 2

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