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

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

Let f(x) = −5x5 + 5x2 − 5x − 4. Find the slope of the graph at x = 1, that is f′(1).

f(x) = −5x5 + 5x2 − 5x − 4x = 1
f′(1) =
3.Medium
xyx = 0.5

Let f(x) = x·sin(3x), with x in radians. Find f′(0.5).

f(x) = x·sin(3x)x = 0.5 rad
f′(0.5) =
4.Medium
xyx = −1

Let f(x) = (2x + 5)5. Find f′(−1).

f(x) = (2x + 5)5x = −1
f′(−1) =
5.Hard
xy

Let f(x) = x3 − 12x2 + 45x − 6. Find the x-coordinate x of the local minimum.

f(x) = x3 − 12x2 + 45x − 6
x =
6.Hard
xy

Let f(x) = x3 + 9x2 + 24x + 2. Find the x-coordinate x of the local maximum.

f(x) = x3 + 9x2 + 24x + 2
x =

Answer key

  1. 1. f′(1) = −11
  2. 2. f′(1) = −20
  3. 3. f′(0.5) = 1.104
  4. 4. f′(−1) = 810
  5. 5. x = 5
  6. 6. x = −4

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