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) = −2x4 − 3x2 + 2x + 4. Find the slope of the graph at x = −2, that is f′(−2).

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

Let f(x) = 5x3 − 4x2 − 9x + 9. Find the slope of the graph at x = −2, that is f′(−2).

f(x) = 5x3 − 4x2 − 9x + 9x = −2
f′(−2) =
3.Medium
xyx = 1

Let f(x) = x·sin(3x), with x in radians. Find f′(1).

f(x) = x·sin(3x)x = 1 rad
f′(1) =
4.Medium
xyx = 1

Let f(x) = x·sin(2x), with x in radians. Find f′(1).

f(x) = x·sin(2x)x = 1 rad
f′(1) =
5.Hard
xyx = 3

The tangent line to f(x) = −x2 + 2x + 1 at x = 3 crosses the y-axis at y = b. Find b.

f(x) = −x2 + 2x + 1x = 3
b =
6.Hard
xy

Let f(x) = x3 + 4.5x2 + 6x + 1. Find the x-coordinate x of the local maximum.

f(x) = x3 + 4.5x2 + 6x + 1
x =

Answer key

  1. 1. f′(−2) = 78
  2. 2. f′(−2) = 67
  3. 3. f′(1) = −2.829
  4. 4. f′(1) = 0.077
  5. 5. b = 10
  6. 6. x = −2

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