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) = −4x3 + 8x2 + 8x + 7. Find the slope of the graph at x = −3, that is f′(−3).

f(x) = −4x3 + 8x2 + 8x + 7x = −3
f′(−3) =
2.Easy
xyx = −2

Let f(x) = −3x3 − 5x2 + 8x − 4. Find the slope of the graph at x = −2, that is f′(−2).

f(x) = −3x3 − 5x2 + 8x − 4x = −2
f′(−2) =
3.Medium
xyx = −2

Let f(x) = ln(3x2 + 1). Find f′(−2).

f(x) = ln(3x2 + 1)x = −2
f′(−2) =
4.Medium
xyx = −1

Let f(x) = (3x − 1)3. Find f′(−1).

f(x) = (3x − 1)3x = −1
f′(−1) =
5.Hard
xy

Let f(x) = x3 + 7.5x2 + 18x − 2. Find the x-coordinate x of the local minimum.

f(x) = x3 + 7.5x2 + 18x − 2
x =
6.Hard
xyx = 3

The tangent line to f(x) = 0.5x2 − 2x − 1 at x = 3 crosses the y-axis at y = b. Find b.

f(x) = 0.5x2 − 2x − 1x = 3
b =

Answer key

  1. 1. f′(−3) = −148
  2. 2. f′(−2) = −8
  3. 3. f′(−2) = −0.9231
  4. 4. f′(−1) = 144
  5. 5. x = −2
  6. 6. b = −5.5

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