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

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

Let f(x) = 4x3 + 4x2 − 7x + 5. Find the slope of the graph at x = 2, that is f′(2).

f(x) = 4x3 + 4x2 − 7x + 5x = 2
f′(2) =
3.Medium
xyx = 0.5

Let f(x) = x2·e2x. Find f′(0.5).

f(x) = x2·e2xx = 0.5
f′(0.5) =
4.Medium
xyx = 0.5

Let f(x) = x·sin(3x), with x in radians. Find f′(0.5).

f(x) = x·sin(3x)x = 0.5 rad
f′(0.5) =
5.Hard
xy

Let f(x) = x3 − 10.5x2 + 30x. Find the x-coordinate x of the local maximum.

f(x) = x3 − 10.5x2 + 30x
x =
6.Hard
xyx = 3

The tangent line to f(x) = 0.5x2 − x − 5 at x = 3 crosses the y-axis at y = b. Find b.

f(x) = 0.5x2 − x − 5x = 3
b =

Answer key

  1. 1. f′(−3) = 1968
  2. 2. f′(2) = 57
  3. 3. f′(0.5) = 4.077
  4. 4. f′(0.5) = 1.104
  5. 5. x = 2
  6. 6. b = −9.5

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