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) = 4x4 + 5x2 + 2x − 4. Find the slope of the graph at x = −3, that is f′(−3).

f(x) = 4x4 + 5x2 + 2x − 4x = −3
f′(−3) =
2.Easy
xyx = 2

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

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

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

The tangent line to f(x) = −x2 + 5x − 2 at x = −2 crosses the y-axis at y = b. Find b.

f(x) = −x2 + 5x − 2x = −2
b =
6.Hard
xyx = 2

The tangent line to f(x) = 0.5x2 − 4x + 5 at x = 2 crosses the y-axis at y = b. Find b.

f(x) = 0.5x2 − 4x + 5x = 2
b =

Answer key

  1. 1. f′(−3) = −460
  2. 2. f′(2) = −110
  3. 3. f′(0.5) = 1.104
  4. 4. f′(2) = 0.8
  5. 5. b = 2
  6. 6. b = 3

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