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) = 4x5 + 9x2 − x − 8. Find the slope of the graph at x = 2, that is f′(2).

f(x) = 4x5 + 9x2 − x − 8x = 2
f′(2) =
2.Easy
xyx = 2

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

f(x) = −5x5 − x2 − 2x − 4x = 2
f′(2) =
3.Medium
xyx = 1.5

Let f(x) = x3·ex. Find f′(1.5).

f(x) = x3·exx = 1.5
f′(1.5) =
4.Medium
xyx = 1

Let f(x) = x3·ex. Find f′(1).

f(x) = x3·exx = 1
f′(1) =
5.Hard
xy

Let f(x) = x3 + 10.5x2 + 36x − 1. Find the x-coordinate x of the local minimum.

f(x) = x3 + 10.5x2 + 36x − 1
x =
6.Hard
xyx = −2

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

f(x) = x2 − 2x + 3x = −2
b =

Answer key

  1. 1. f′(2) = 355
  2. 2. f′(2) = −406
  3. 3. f′(1.5) = 45.38
  4. 4. f′(1) = 10.87
  5. 5. x = −3
  6. 6. b = −1

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