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) = x5 − 3x2 − 2x − 1. Find the slope of the graph at x = 3, that is f′(3).

f(x) = x5 − 3x2 − 2x − 1x = 3
f′(3) =
2.Easy
xyx = −2

Let f(x) = −4x3 − x2 + 7x − 3. Find the slope of the graph at x = −2, that is f′(−2).

f(x) = −4x3 − x2 + 7x − 3x = −2
f′(−2) =
3.Medium
xyx = 1

Let f(x) = x·sin(3x), with x in radians. Find f′(1).

f(x) = x·sin(3x)x = 1 rad
f′(1) =
4.Medium
xyx = 1.5

Let f(x) = x2·e0.5x. Find f′(1.5).

f(x) = x2·e0.5xx = 1.5
f′(1.5) =
5.Hard
xy

Let f(x) = x3 + 6x2 + 9x − 4. Find the x-coordinate x of the local minimum.

f(x) = x3 + 6x2 + 9x − 4
x =
6.Hard
xy

Let f(x) = x3 + 3x2 − 9x − 1. Find the x-coordinate x of the local minimum.

f(x) = x3 + 3x2 − 9x − 1
x =

Answer key

  1. 1. f′(3) = 385
  2. 2. f′(−2) = −37
  3. 3. f′(1) = −2.829
  4. 4. f′(1.5) = 8.733
  5. 5. x = −1
  6. 6. x = 1

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