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) = 5x4 − 4x2 − 2x + 8. Find the slope of the graph at x = 2, that is f′(2).

f(x) = 5x4 − 4x2 − 2x + 8x = 2
f′(2) =
2.Easy
xyx = 3

Let f(x) = −x4 − 4x2 + 5x − 8. Find the slope of the graph at x = 3, that is f′(3).

f(x) = −x4 − 4x2 + 5x − 8x = 3
f′(3) =
3.Medium
xyx = 1

Let f(x) = x2·e0.5x. Find f′(1).

f(x) = x2·e0.5xx = 1
f′(1) =
4.Medium
xyx = 2

Let f(x) = x·sin(x), with x in radians. Find f′(2).

f(x) = x·sin(x)x = 2 rad
f′(2) =
5.Hard
xyx = 1

The tangent line to f(x) = 3x2 − x at x = 1 crosses the y-axis at y = b. Find b.

f(x) = 3x2 − xx = 1
b =
6.Hard
xy

Let f(x) = x3 + 7.5x2 + 12x − 1. Find the x-coordinate x of the local maximum.

f(x) = x3 + 7.5x2 + 12x − 1
x =

Answer key

  1. 1. f′(2) = 142
  2. 2. f′(3) = −127
  3. 3. f′(1) = 4.122
  4. 4. f′(2) = 0.077
  5. 5. b = −3
  6. 6. x = −4

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