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 = 1

Let f(x) = −5x3 + 9x2 + 3. Find the slope of the graph at x = 1, that is f′(1).

f(x) = −5x3 + 9x2 + 3x = 1
f′(1) =
2.Easy
xyx = 2

Let f(x) = −2x4 + 3x2 − 4x − 9. Find the slope of the graph at x = 2, that is f′(2).

f(x) = −2x4 + 3x2 − 4x − 9x = 2
f′(2) =
3.Medium
xyx = 1

Let f(x) = (3x − 1)4. Find f′(1).

f(x) = (3x − 1)4x = 1
f′(1) =
4.Medium
xyx = 0.5

Let f(x) = x3·e2x. Find f′(0.5).

f(x) = x3·e2xx = 0.5
f′(0.5) =
5.Hard
xyx = 2

The tangent line to f(x) = −x2 + 4x − 6 at x = 2 crosses the y-axis at y = b. Find b.

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

The tangent line to f(x) = x2 − x + 6 at x = 2 crosses the y-axis at y = b. Find b.

f(x) = x2 − x + 6x = 2
b =

Answer key

  1. 1. f′(1) = 3
  2. 2. f′(2) = −56
  3. 3. f′(1) = 96
  4. 4. f′(0.5) = 2.718
  5. 5. b = −2
  6. 6. b = 2

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