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) = −2x4 + 7x2 + 4. Find the slope of the graph at x = 3, that is f′(3).

f(x) = −2x4 + 7x2 + 4x = 3
f′(3) =
2.Easy
xyx = 3

Let f(x) = 2x5 + 3x2 − 6x − 9. Find the slope of the graph at x = 3, that is f′(3).

f(x) = 2x5 + 3x2 − 6x − 9x = 3
f′(3) =
3.Medium
xyx = 1.5

Let f(x) = x3·e−0.5x. Find f′(1.5).

f(x) = x3·e−0.5xx = 1.5
f′(1.5) =
4.Medium
xyx = 2

Let f(x) = (3x + 1)4. Find f′(2).

f(x) = (3x + 1)4x = 2
f′(2) =
5.Hard
xyx = 1

The tangent line to f(x) = 0.5x2 − x − 2 at x = 1 crosses the y-axis at y = b. Find b.

f(x) = 0.5x2 − x − 2x = 1
b =
6.Hard
xyx = 2

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

f(x) = −x2 + 3x + 2x = 2
b =

Answer key

  1. 1. f′(3) = −174
  2. 2. f′(3) = 822
  3. 3. f′(1.5) = 2.391
  4. 4. f′(2) = 4116
  5. 5. b = −2.5
  6. 6. b = 6

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