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 − 4x2 − 9x + 8. Find the slope of the graph at x = 2, that is f′(2).

f(x) = −4x4 − 4x2 − 9x + 8x = 2
f′(2) =
2.Easy
xyx = −1

Let f(x) = −5x5 + x2 − 9x + 8. Find the slope of the graph at x = −1, that is f′(−1).

f(x) = −5x5 + x2 − 9x + 8x = −1
f′(−1) =
3.Medium
xyx = 1

Let f(x) = (2x + 3)3. Find f′(1).

f(x) = (2x + 3)3x = 1
f′(1) =
4.Medium
xyx = 0.5

Let f(x) = x·sin(x), with x in radians. Find f′(0.5).

f(x) = x·sin(x)x = 0.5 rad
f′(0.5) =
5.Hard
xyx = 3

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

f(x) = 3x2 + x − 2x = 3
b =
6.Hard
xy

Let f(x) = x3 − 13.5x2 + 54x − 5. Find the x-coordinate x of the local minimum.

f(x) = x3 − 13.5x2 + 54x − 5
x =

Answer key

  1. 1. f′(2) = −153
  2. 2. f′(−1) = −36
  3. 3. f′(1) = 150
  4. 4. f′(0.5) = 0.9182
  5. 5. b = −29
  6. 6. x = 6

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