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) = 4x4 + 5x2 + 6x. Find the slope of the graph at x = 2, that is f′(2).

f(x) = 4x4 + 5x2 + 6xx = 2
f′(2) =
2.Easy
xyx = −1

Let f(x) = −2x5 − 7x2 + x + 6. Find the slope of the graph at x = −1, that is f′(−1).

f(x) = −2x5 − 7x2 + x + 6x = −1
f′(−1) =
3.Medium
xyx = 0

Let f(x) = (3x − 1)4. Find f′(0).

f(x) = (3x − 1)4x = 0
f′(0) =
4.Medium
xyx = −2

Let f(x) = ln(2x2 + 2). Find f′(−2).

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

The tangent line to f(x) = 0.5x2 + 4x − 2 at x = 2 crosses the y-axis at y = b. Find b.

f(x) = 0.5x2 + 4x − 2x = 2
b =
6.Hard
xy

Let f(x) = x3 − 1.5x2 − 6x + 2. Find the x-coordinate x of the local minimum.

f(x) = x3 − 1.5x2 − 6x + 2
x =

Answer key

  1. 1. f′(2) = 154
  2. 2. f′(−1) = 5
  3. 3. f′(0) = −12
  4. 4. f′(−2) = −0.8
  5. 5. b = −4
  6. 6. x = 2

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