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) = 3x4 + 6x2 + 9x + 5. Find the slope of the graph at x = −1, that is f′(−1).

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

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

f(x) = x3 + 9x2 + 5x + 9x = −3
f′(−3) =
3.Medium
xyx = 0.5

Let f(x) = x2·e−x. Find f′(0.5).

f(x) = x2·e−xx = 0.5
f′(0.5) =
4.Medium
xyx = 2

Let f(x) = ln(2x2 + 2). Find f′(2).

f(x) = ln(2x2 + 2)x = 2
f′(2) =
5.Hard
xyx = 2

The tangent line to f(x) = 3x2 + 5x + 1 at x = 2 crosses the y-axis at y = b. Find b.

f(x) = 3x2 + 5x + 1x = 2
b =
6.Hard
xy

Let f(x) = x3 − 4.5x2 + 6x − 4. Find the x-coordinate x of the local minimum.

f(x) = x3 − 4.5x2 + 6x − 4
x =

Answer key

  1. 1. f′(−1) = −15
  2. 2. f′(−3) = −22
  3. 3. f′(0.5) = 0.4549
  4. 4. f′(2) = 0.8
  5. 5. b = −11
  6. 6. x = 2

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