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

f(x) = x5 − x2 − 2x − 9x = 3
f′(3) =
2.Easy
xyx = −1

Let f(x) = x4 + 3x2 + 6x − 1. Find the slope of the graph at x = −1, that is f′(−1).

f(x) = x4 + 3x2 + 6x − 1x = −1
f′(−1) =
3.Medium
xyx = 0.5

Let f(x) = x·e2x. Find f′(0.5).

f(x) = x·e2xx = 0.5
f′(0.5) =
4.Medium
xyx = 2

Let f(x) = x·sin(3x), with x in radians. Find f′(2).

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

The tangent line to f(x) = x2 − x + 4 at x = −1 crosses the y-axis at y = b. Find b.

f(x) = x2 − x + 4x = −1
b =
6.Hard
xy

Let f(x) = x3 − 3x2 + 1. Find the x-coordinate x of the local minimum.

f(x) = x3 − 3x2 + 1
x =

Answer key

  1. 1. f′(3) = 397
  2. 2. f′(−1) = −4
  3. 3. f′(0.5) = 5.437
  4. 4. f′(2) = 5.482
  5. 5. b = 3
  6. 6. x = 2

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