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) = 3x5 + 7x2 − 4x + 9. Find the slope of the graph at x = 2, that is f′(2).

f(x) = 3x5 + 7x2 − 4x + 9x = 2
f′(2) =
2.Easy
xyx = −1

Let f(x) = −2x5 + 6x2 + 4x − 4. Find the slope of the graph at x = −1, that is f′(−1).

f(x) = −2x5 + 6x2 + 4x − 4x = −1
f′(−1) =
3.Medium
xyx = −1

Let f(x) = ln(2x2 + 4). Find f′(−1).

f(x) = ln(2x2 + 4)x = −1
f′(−1) =
4.Medium
xyx = 2

Let f(x) = x·e2x. Find f′(2).

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

The tangent line to f(x) = −x2 + 3x − 5 at x = −2 crosses the y-axis at y = b. Find b.

f(x) = −x2 + 3x − 5x = −2
b =
6.Hard
xyx = 3

The tangent line to f(x) = 2x2 − x + 6 at x = 3 crosses the y-axis at y = b. Find b.

f(x) = 2x2 − x + 6x = 3
b =

Answer key

  1. 1. f′(2) = 264
  2. 2. f′(−1) = −18
  3. 3. f′(−1) = −0.6667
  4. 4. f′(2) = 273
  5. 5. b = −1
  6. 6. b = −12

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