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) = 2x5 + 4x2 + 8x − 8. Find the slope of the graph at x = 3, that is f′(3).

f(x) = 2x5 + 4x2 + 8x − 8x = 3
f′(3) =
2.Easy
xyx = −3

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

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

Let f(x) = x·sin(3x), with x in radians. Find f′(2).

f(x) = x·sin(3x)x = 2 rad
f′(2) =
4.Medium
xyx = 1.5

Let f(x) = x·e2x. Find f′(1.5).

f(x) = x·e2xx = 1.5
f′(1.5) =
5.Hard
xy

Let f(x) = x3 − 10.5x2 + 30x + 1. Find the x-coordinate x of the local minimum.

f(x) = x3 − 10.5x2 + 30x + 1
x =
6.Hard
xy

Let f(x) = x3 + 6x2 + 9x − 2. Find the x-coordinate x of the local maximum.

f(x) = x3 + 6x2 + 9x − 2
x =

Answer key

  1. 1. f′(3) = 842
  2. 2. f′(−3) = −59
  3. 3. f′(2) = 5.482
  4. 4. f′(1.5) = 80.34
  5. 5. x = 5
  6. 6. x = −3

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