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) = −5x3 − 8x2 + 7x + 4. Find the slope of the graph at x = 3, that is f′(3).

f(x) = −5x3 − 8x2 + 7x + 4x = 3
f′(3) =
2.Easy
xyx = 1

Let f(x) = 3x5 + 5x2 + 6x − 9. Find the slope of the graph at x = 1, that is f′(1).

f(x) = 3x5 + 5x2 + 6x − 9x = 1
f′(1) =
3.Medium
xyx = 2

Let f(x) = (3x + 5)5. Find f′(2).

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

Let f(x) = x2·e0.5x. Find f′(1).

f(x) = x2·e0.5xx = 1
f′(1) =
5.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 =
6.Hard
xy

Let f(x) = x3 − 12x + 2. Find the x-coordinate x of the local minimum.

f(x) = x3 − 12x + 2
x =

Answer key

  1. 1. f′(3) = −176
  2. 2. f′(1) = 31
  3. 3. f′(2) = 219615
  4. 4. f′(1) = 4.122
  5. 5. x = −4
  6. 6. x = 2

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