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 = −2

Let f(x) = 5x5 − 9x2 − 3x + 1. Find the slope of the graph at x = −2, that is f′(−2).

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

Let f(x) = −5x5 + 3x2 − 8x + 4. Find the slope of the graph at x = −2, that is f′(−2).

f(x) = −5x5 + 3x2 − 8x + 4x = −2
f′(−2) =
3.Medium
xyx = 0

Let f(x) = (2x + 3)3. Find f′(0).

f(x) = (2x + 3)3x = 0
f′(0) =
4.Medium
xyx = −2

Let f(x) = ln(3x2 + 2). Find f′(−2).

f(x) = ln(3x2 + 2)x = −2
f′(−2) =
5.Hard
xy

Let f(x) = x3 − 9x2 + 24x − 5. Find the x-coordinate x of the local maximum.

f(x) = x3 − 9x2 + 24x − 5
x =
6.Hard
xy

Let f(x) = x3 − 9x2 + 15x − 3. Find the x-coordinate x of the local maximum.

f(x) = x3 − 9x2 + 15x − 3
x =

Answer key

  1. 1. f′(−2) = 433
  2. 2. f′(−2) = −420
  3. 3. f′(0) = 54
  4. 4. f′(−2) = −0.8571
  5. 5. x = 2
  6. 6. x = 1

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