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) = 2x3 + 2x2 + 6x − 8. Find the slope of the graph at x = −3, that is f′(−3).

f(x) = 2x3 + 2x2 + 6x − 8x = −3
f′(−3) =
2.Easy
xyx = −2

Let f(x) = −x4 + 8x2 + 4x − 5. Find the slope of the graph at x = −2, that is f′(−2).

f(x) = −x4 + 8x2 + 4x − 5x = −2
f′(−2) =
3.Medium
xyx = 3

Let f(x) = ln(3x2 + 4). Find f′(3).

f(x) = ln(3x2 + 4)x = 3
f′(3) =
4.Medium
xyx = 1.5

Let f(x) = x·sin(3x), with x in radians. Find f′(1.5).

f(x) = x·sin(3x)x = 1.5 rad
f′(1.5) =
5.Hard
xy

Let f(x) = x3 − 12x2 + 36x + 6. Find the x-coordinate x of the local maximum.

f(x) = x3 − 12x2 + 36x + 6
x =
6.Hard
xyx = 1

The tangent line to f(x) = 3x2 + 2 at x = 1 crosses the y-axis at y = b. Find b.

f(x) = 3x2 + 2x = 1
b =

Answer key

  1. 1. f′(−3) = 48
  2. 2. f′(−2) = 4
  3. 3. f′(3) = 0.5806
  4. 4. f′(1.5) = −1.926
  5. 5. x = 2
  6. 6. b = −1

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