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 + 1. Find the slope of the graph at x = 2, that is f′(2).

f(x) = −2x4 − 3x2 + 1x = 2
f′(2) =
2.Easy
xyx = −3

Let f(x) = −x3 − x2 − 2x − 1. Find the slope of the graph at x = −3, that is f′(−3).

f(x) = −x3 − x2 − 2x − 1x = −3
f′(−3) =
3.Medium
xyx = 0.5

Let f(x) = x·sin(3x), with x in radians. Find f′(0.5).

f(x) = x·sin(3x)x = 0.5 rad
f′(0.5) =
4.Medium
xyx = −2

Let f(x) = ln(x2 + 4). Find f′(−2).

f(x) = ln(x2 + 4)x = −2
f′(−2) =
5.Hard
xyx = 3

The tangent line to f(x) = 0.5x2 − 5x + 5 at x = 3 crosses the y-axis at y = b. Find b.

f(x) = 0.5x2 − 5x + 5x = 3
b =
6.Hard
xyx = 1

The tangent line to f(x) = 0.5x2 − 4x − 3 at x = 1 crosses the y-axis at y = b. Find b.

f(x) = 0.5x2 − 4x − 3x = 1
b =

Answer key

  1. 1. f′(2) = −76
  2. 2. f′(−3) = −23
  3. 3. f′(0.5) = 1.104
  4. 4. f′(−2) = −0.5
  5. 5. b = 0.5
  6. 6. b = −3.5

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