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) = −2x3 − 6x2 − 7. Find the slope of the graph at x = −3, that is f′(−3).

f(x) = −2x3 − 6x2 − 7x = −3
f′(−3) =
2.Easy
xyx = 1

Let f(x) = 3x3 + 7x2 + 4x − 8. Find the slope of the graph at x = 1, that is f′(1).

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

f(x) = (4x + 3)5x = 1
f′(1) =
5.Hard
xy

Let f(x) = x3 − 3x − 5. Find the x-coordinate x of the local minimum.

f(x) = x3 − 3x − 5
x =
6.Hard
xy

Let f(x) = x3 + 4.5x2 + 6x − 5. Find the x-coordinate x of the local minimum.

f(x) = x3 + 4.5x2 + 6x − 5
x =

Answer key

  1. 1. f′(−3) = −18
  2. 2. f′(1) = 27
  3. 3. f′(−2) = −0.6667
  4. 4. f′(1) = 48020
  5. 5. x = 1
  6. 6. x = −1

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