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

f(x) = −5x3 + 4x2 − 1x = 2
f′(2) =
2.Easy
xyx = −3

Let f(x) = −2x4 + 3x2 − 5x + 3. Find the slope of the graph at x = −3, that is f′(−3).

f(x) = −2x4 + 3x2 − 5x + 3x = −3
f′(−3) =
3.Medium
xyx = 1.5

Let f(x) = x·e−x. Find f′(1.5).

f(x) = x·e−xx = 1.5
f′(1.5) =
4.Medium
xyx = −1

Let f(x) = (4x + 5)5. Find f′(−1).

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

The tangent line to f(x) = x2 + 5x − 6 at x = 1 crosses the y-axis at y = b. Find b.

f(x) = x2 + 5x − 6x = 1
b =
6.Hard
xyx = 3

The tangent line to f(x) = 2x2 + 1 at x = 3 crosses the y-axis at y = b. Find b.

f(x) = 2x2 + 1x = 3
b =

Answer key

  1. 1. f′(2) = −44
  2. 2. f′(−3) = 193
  3. 3. f′(1.5) = −0.1116
  4. 4. f′(−1) = 20
  5. 5. b = −7
  6. 6. b = −17

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