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 = −2

Let f(x) = −3x3 + 7x2 − 7x + 1. Find the slope of the graph at x = −2, that is f′(−2).

f(x) = −3x3 + 7x2 − 7x + 1x = −2
f′(−2) =
2.Easy
xyx = −1

Let f(x) = −5x3 + 2x2 + 7x + 3. Find the slope of the graph at x = −1, that is f′(−1).

f(x) = −5x3 + 2x2 + 7x + 3x = −1
f′(−1) =
3.Medium
xyx = 0

Let f(x) = (2x − 3)3. Find f′(0).

f(x) = (2x − 3)3x = 0
f′(0) =
4.Medium
xyx = −1

Let f(x) = ln(3x2 + 2). Find f′(−1).

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

The tangent line to f(x) = 3x2 + x − 4 at x = 2 crosses the y-axis at y = b. Find b.

f(x) = 3x2 + x − 4x = 2
b =
6.Hard
xyx = 3

The tangent line to f(x) = 3x2 + 4x − 2 at x = 3 crosses the y-axis at y = b. Find b.

f(x) = 3x2 + 4x − 2x = 3
b =

Answer key

  1. 1. f′(−2) = −71
  2. 2. f′(−1) = −12
  3. 3. f′(0) = 54
  4. 4. f′(−1) = −1.2
  5. 5. b = −16
  6. 6. b = −29

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