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) = x3 − 3x2 + 9x − 4. Find the slope of the graph at x = −1, that is f′(−1).

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

Let f(x) = 2x4 + 8x2 + 7x − 4. Find the slope of the graph at x = 2, that is f′(2).

f(x) = 2x4 + 8x2 + 7x − 4x = 2
f′(2) =
3.Medium
xyx = 3

Let f(x) = ln(3x2 + 2). Find f′(3).

f(x) = ln(3x2 + 2)x = 3
f′(3) =
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
xy

Let f(x) = x3 − 7.5x2 + 18x + 3. Find the x-coordinate x of the local minimum.

f(x) = x3 − 7.5x2 + 18x + 3
x =
6.Hard
xyx = 1

The tangent line to f(x) = 0.5x2 − 2x + 6 at x = 1 crosses the y-axis at y = b. Find b.

f(x) = 0.5x2 − 2x + 6x = 1
b =

Answer key

  1. 1. f′(−1) = 18
  2. 2. f′(2) = 103
  3. 3. f′(3) = 0.6207
  4. 4. f′(0.5) = 0.9182
  5. 5. x = 3
  6. 6. b = 5.5

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