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

f(x) = 4x4 − x2 − 6x + 1x = −3
f′(−3) =
2.Easy
xyx = 3

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

f(x) = −x5 − 2x2 − 3x + 3x = 3
f′(3) =
3.Medium
xyx = −2

Let f(x) = ln(3x2 + 4). Find f′(−2).

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

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

f(x) = x·sin(x)x = 2 rad
f′(2) =
5.Hard
xy

Let f(x) = x3 − 9x2 + 15x − 2. Find the x-coordinate x of the local maximum.

f(x) = x3 − 9x2 + 15x − 2
x =
6.Hard
xyx = 3

The tangent line to f(x) = 0.5x2 + 2x at x = 3 crosses the y-axis at y = b. Find b.

f(x) = 0.5x2 + 2xx = 3
b =

Answer key

  1. 1. f′(−3) = −432
  2. 2. f′(3) = −420
  3. 3. f′(−2) = −0.75
  4. 4. f′(2) = 0.077
  5. 5. x = 1
  6. 6. b = −4.5

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