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

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

Let f(x) = −4x5 − 5x2 − x − 6. Find the slope of the graph at x = 1, that is f′(1).

f(x) = −4x5 − 5x2 − x − 6x = 1
f′(1) =
3.Medium
xyx = 2

Let f(x) = (2x − 1)4. Find f′(2).

f(x) = (2x − 1)4x = 2
f′(2) =
4.Medium
xyx = 2

Let f(x) = ln(2x2 + 4). Find f′(2).

f(x) = ln(2x2 + 4)x = 2
f′(2) =
5.Hard
xy

Let f(x) = x3 + 4.5x2 + 6x − 2. Find the x-coordinate x of the local maximum.

f(x) = x3 + 4.5x2 + 6x − 2
x =
6.Hard
xy

Let f(x) = x3 − 4.5x2 + 6x + 3. Find the x-coordinate x of the local maximum.

f(x) = x3 − 4.5x2 + 6x + 3
x =

Answer key

  1. 1. f′(3) = 176
  2. 2. f′(1) = −31
  3. 3. f′(2) = 216
  4. 4. f′(2) = 0.6667
  5. 5. x = −2
  6. 6. x = 1

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