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) = 3x5 + 5x2 − 6x − 2. Find the slope of the graph at x = −1, that is f′(−1).

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

Let f(x) = 2x3 + 6x2 − 4x + 9. Find the slope of the graph at x = −1, that is f′(−1).

f(x) = 2x3 + 6x2 − 4x + 9x = −1
f′(−1) =
3.Medium
xyx = 2

Let f(x) = (−2x + 5)3. Find f′(2).

f(x) = (−2x + 5)3x = 2
f′(2) =
4.Medium
xyx = 2

Let f(x) = x·ex. Find f′(2).

f(x) = x·exx = 2
f′(2) =
5.Hard
xy

Let f(x) = x3 − 12x2 + 45x + 5. Find the x-coordinate x of the local maximum.

f(x) = x3 − 12x2 + 45x + 5
x =
6.Hard
xyx = 2

The tangent line to f(x) = 0.5x2 − 5x + 3 at x = 2 crosses the y-axis at y = b. Find b.

f(x) = 0.5x2 − 5x + 3x = 2
b =

Answer key

  1. 1. f′(−1) = −1
  2. 2. f′(−1) = −10
  3. 3. f′(2) = −6
  4. 4. f′(2) = 22.17
  5. 5. x = 3
  6. 6. b = 1

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