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) = x4 + 5x2 + 5x − 3. Find the slope of the graph at x = −1, that is f′(−1).

f(x) = x4 + 5x2 + 5x − 3x = −1
f′(−1) =
2.Easy
xyx = 2

Let f(x) = −3x5 − 7x2 − 6x − 9. Find the slope of the graph at x = 2, that is f′(2).

f(x) = −3x5 − 7x2 − 6x − 9x = 2
f′(2) =
3.Medium
xyx = −2

Let f(x) = ln(x2 + 2). Find f′(−2).

f(x) = ln(x2 + 2)x = −2
f′(−2) =
4.Medium
xyx = 1

Let f(x) = ln(x2 + 2). Find f′(1).

f(x) = ln(x2 + 2)x = 1
f′(1) =
5.Hard
xy

Let f(x) = x3 − 12x − 5. Find the x-coordinate x of the local maximum.

f(x) = x3 − 12x − 5
x =
6.Hard
xy

Let f(x) = x3 − 13.5x2 + 54x − 2. Find the x-coordinate x of the local maximum.

f(x) = x3 − 13.5x2 + 54x − 2
x =

Answer key

  1. 1. f′(−1) = −9
  2. 2. f′(2) = −274
  3. 3. f′(−2) = −0.6667
  4. 4. f′(1) = 0.6667
  5. 5. x = −2
  6. 6. x = 3

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