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) = −3x4 + 9x2 − 4x − 2. Find the slope of the graph at x = −3, that is f′(−3).

f(x) = −3x4 + 9x2 − 4x − 2x = −3
f′(−3) =
2.Easy
xyx = −1

Let f(x) = 5x4 + 7x2 − 8x + 2. Find the slope of the graph at x = −1, that is f′(−1).

f(x) = 5x4 + 7x2 − 8x + 2x = −1
f′(−1) =
3.Medium
xyx = −1

Let f(x) = ln(3x2 + 5). Find f′(−1).

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

Let f(x) = x2·e−0.5x. Find f′(2).

f(x) = x2·e−0.5xx = 2
f′(2) =
5.Hard
xy

Let f(x) = x3 − 1.5x2 − 6x + 2. Find the x-coordinate x of the local maximum.

f(x) = x3 − 1.5x2 − 6x + 2
x =
6.Hard
xy

Let f(x) = x3 − 10.5x2 + 30x − 6. Find the x-coordinate x of the local minimum.

f(x) = x3 − 10.5x2 + 30x − 6
x =

Answer key

  1. 1. f′(−3) = 266
  2. 2. f′(−1) = −42
  3. 3. f′(−1) = −0.75
  4. 4. f′(2) = 0.7358
  5. 5. x = −1
  6. 6. x = 5

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