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) = −x5 − 4x2 − x + 9. Find the slope of the graph at x = 3, that is f′(3).

f(x) = −x5 − 4x2 − x + 9x = 3
f′(3) =
2.Easy
xyx = 2

Let f(x) = x3 − 8x2 + 9x − 2. Find the slope of the graph at x = 2, that is f′(2).

f(x) = x3 − 8x2 + 9x − 2x = 2
f′(2) =
3.Medium
xyx = 0

Let f(x) = (3x + 3)5. Find f′(0).

f(x) = (3x + 3)5x = 0
f′(0) =
4.Medium
xyx = 2

Let f(x) = ln(3x2 + 2). Find f′(2).

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

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

f(x) = 0.5x2 − 3x − 3x = 2
b =
6.Hard
xyx = 2

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

f(x) = 3x2 − 3x + 4x = 2
b =

Answer key

  1. 1. f′(3) = −430
  2. 2. f′(2) = −11
  3. 3. f′(0) = 1215
  4. 4. f′(2) = 0.8571
  5. 5. b = −5
  6. 6. b = −8

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