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) = 4x5 + 5x2 − 2x − 9. Find the slope of the graph at x = 3, that is f′(3).

f(x) = 4x5 + 5x2 − 2x − 9x = 3
f′(3) =
2.Easy
xyx = −2

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

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

Let f(x) = (−2x − 3)4. Find f′(1).

f(x) = (−2x − 3)4x = 1
f′(1) =
4.Medium
xyx = 1

Let f(x) = x2·e−0.5x. Find f′(1).

f(x) = x2·e−0.5xx = 1
f′(1) =
5.Hard
xy

Let f(x) = x3 − 6x2 + 9x − 3. Find the x-coordinate x of the local minimum.

f(x) = x3 − 6x2 + 9x − 3
x =
6.Hard
xyx = −2

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

f(x) = 2x2 + x − 5x = −2
b =

Answer key

  1. 1. f′(3) = 1648
  2. 2. f′(−2) = 231
  3. 3. f′(1) = 1000
  4. 4. f′(1) = 0.9098
  5. 5. x = 3
  6. 6. b = −13

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