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) = −4x3 + 9x2 − 5x − 1. Find the slope of the graph at x = 2, that is f′(2).

f(x) = −4x3 + 9x2 − 5x − 1x = 2
f′(2) =
2.Easy
xyx = 1

Let f(x) = −4x3 − 9x2 − 8x + 7. Find the slope of the graph at x = 1, that is f′(1).

f(x) = −4x3 − 9x2 − 8x + 7x = 1
f′(1) =
3.Medium
xyx = 2

Let f(x) = x3·e−0.5x. Find f′(2).

f(x) = x3·e−0.5xx = 2
f′(2) =
4.Medium
xyx = −1

Let f(x) = (2x − 3)5. Find f′(−1).

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

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

f(x) = 2x2 − xx = −1
b =
6.Hard
xyx = 3

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

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

Answer key

  1. 1. f′(2) = −17
  2. 2. f′(1) = −38
  3. 3. f′(2) = 2.943
  4. 4. f′(−1) = 6250
  5. 5. b = −2
  6. 6. b = −7

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