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) = −5x4 + 2x2 − 6x − 9. Find the slope of the graph at x = −1, that is f′(−1).

f(x) = −5x4 + 2x2 − 6x − 9x = −1
f′(−1) =
2.Easy
xyx = 3

Let f(x) = 3x4 + x2 − 3x + 8. Find the slope of the graph at x = 3, that is f′(3).

f(x) = 3x4 + x2 − 3x + 8x = 3
f′(3) =
3.Medium
xyx = −1

Let f(x) = ln(x2 + 4). Find f′(−1).

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

Let f(x) = x·e−x. Find f′(2).

f(x) = x·e−xx = 2
f′(2) =
5.Hard
xyx = −1

The tangent line to f(x) = −x2 + 2x − 4 at x = −1 crosses the y-axis at y = b. Find b.

f(x) = −x2 + 2x − 4x = −1
b =
6.Hard
xyx = −2

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

f(x) = 3x2 + 2x + 5x = −2
b =

Answer key

  1. 1. f′(−1) = 10
  2. 2. f′(3) = 327
  3. 3. f′(−1) = −0.4
  4. 4. f′(2) = −0.1353
  5. 5. b = −3
  6. 6. b = −7

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