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) = −2x4 − 4x2 − 2x − 6. Find the slope of the graph at x = −1, that is f′(−1).

f(x) = −2x4 − 4x2 − 2x − 6x = −1
f′(−1) =
2.Easy
xyx = 3

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

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

Let f(x) = ln(2x2 + 2). Find f′(1).

f(x) = ln(2x2 + 2)x = 1
f′(1) =
4.Medium
xyx = 1.5

Let f(x) = x2·e−x. Find f′(1.5).

f(x) = x2·e−xx = 1.5
f′(1.5) =
5.Hard
xy

Let f(x) = x3 − 7.5x2 + 12x − 5. Find the x-coordinate x of the local maximum.

f(x) = x3 − 7.5x2 + 12x − 5
x =
6.Hard
xyx = 2

The tangent line to f(x) = 3x2 − x − 6 at x = 2 crosses the y-axis at y = b. Find b.

f(x) = 3x2 − x − 6x = 2
b =

Answer key

  1. 1. f′(−1) = 14
  2. 2. f′(3) = 1239
  3. 3. f′(1) = 1
  4. 4. f′(1.5) = 0.1673
  5. 5. x = 1
  6. 6. b = −18

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