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) = 5x4 + 8x2 − 7x − 9. Find the slope of the graph at x = −1, that is f′(−1).

f(x) = 5x4 + 8x2 − 7x − 9x = −1
f′(−1) =
2.Easy
xyx = 2

Let f(x) = −5x5 + 2x2 + 9x + 7. Find the slope of the graph at x = 2, that is f′(2).

f(x) = −5x5 + 2x2 + 9x + 7x = 2
f′(2) =
3.Medium
xyx = 0.5

Let f(x) = x3·e−0.5x. Find f′(0.5).

f(x) = x3·e−0.5xx = 0.5
f′(0.5) =
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
xyx = −2

The tangent line to f(x) = 0.5x2 − 5x + 4 at x = −2 crosses the y-axis at y = b. Find b.

f(x) = 0.5x2 − 5x + 4x = −2
b =
6.Hard
xy

Let f(x) = x3 − 12x2 + 36x + 5. Find the x-coordinate x of the local minimum.

f(x) = x3 − 12x2 + 36x + 5
x =

Answer key

  1. 1. f′(−1) = −43
  2. 2. f′(2) = −383
  3. 3. f′(0.5) = 0.5354
  4. 4. f′(1) = 0.9098
  5. 5. b = 2
  6. 6. x = 6

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