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) = −2x3 + 6x2 − 4x − 8. Find the slope of the graph at x = −1, that is f′(−1).

f(x) = −2x3 + 6x2 − 4x − 8x = −1
f′(−1) =
2.Easy
xyx = 3

Let f(x) = x5 + 3x2 + 4x − 7. Find the slope of the graph at x = 3, that is f′(3).

f(x) = x5 + 3x2 + 4x − 7x = 3
f′(3) =
3.Medium
xyx = 1.5

Let f(x) = x3·e2x. Find f′(1.5).

f(x) = x3·e2xx = 1.5
f′(1.5) =
4.Medium
xyx = 0

Let f(x) = (2x + 5)5. Find f′(0).

f(x) = (2x + 5)5x = 0
f′(0) =
5.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 =
6.Hard
xyx = 3

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

f(x) = −x2 + 2x − 3x = 3
b =

Answer key

  1. 1. f′(−1) = −22
  2. 2. f′(3) = 427
  3. 3. f′(1.5) = 271.2
  4. 4. f′(0) = 6250
  5. 5. x = 6
  6. 6. b = 6

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