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 − 4x2 + 2x + 1. Find the slope of the graph at x = −3, that is f′(−3).

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

Let f(x) = 3x3 + 8x2 + 7x + 6. Find the slope of the graph at x = −3, that is f′(−3).

f(x) = 3x3 + 8x2 + 7x + 6x = −3
f′(−3) =
3.Medium
xyx = −2

Let f(x) = ln(3x2 + 5). Find f′(−2).

f(x) = ln(3x2 + 5)x = −2
f′(−2) =
4.Medium
xyx = −1

Let f(x) = (−2x + 5)4. Find f′(−1).

f(x) = (−2x + 5)4x = −1
f′(−1) =
5.Hard
xyx = −1

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

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

The tangent line to f(x) = 3x2 − 5x − 1 at x = 1 crosses the y-axis at y = b. Find b.

f(x) = 3x2 − 5x − 1x = 1
b =

Answer key

  1. 1. f′(−3) = −406
  2. 2. f′(−3) = 40
  3. 3. f′(−2) = −0.7059
  4. 4. f′(−1) = −2744
  5. 5. b = −3.5
  6. 6. b = −4

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