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) = −5x3 − 6x2 + 4x − 4. Find the slope of the graph at x = 2, that is f′(2).

f(x) = −5x3 − 6x2 + 4x − 4x = 2
f′(2) =
2.Easy
xyx = 1

Let f(x) = −x4 + 7x2 + 8x + 7. Find the slope of the graph at x = 1, that is f′(1).

f(x) = −x4 + 7x2 + 8x + 7x = 1
f′(1) =
3.Medium
xyx = −2

Let f(x) = ln(3x2 + 2). Find f′(−2).

f(x) = ln(3x2 + 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 + 4.5x2 + 6x − 6. Find the x-coordinate x of the local minimum.

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

Let f(x) = x3 − 3x2 − 4. Find the x-coordinate x of the local minimum.

f(x) = x3 − 3x2 − 4
x =

Answer key

  1. 1. f′(2) = −80
  2. 2. f′(1) = 18
  3. 3. f′(−2) = −0.8571
  4. 4. f′(1) = 0.6667
  5. 5. x = −1
  6. 6. x = 2

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