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

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

Let f(x) = −4x5 + 8x2 + 4x + 8. Find the slope of the graph at x = −3, that is f′(−3).

f(x) = −4x5 + 8x2 + 4x + 8x = −3
f′(−3) =
3.Medium
xyx = 0.5

Let f(x) = x·sin(2x), with x in radians. Find f′(0.5).

f(x) = x·sin(2x)x = 0.5 rad
f′(0.5) =
4.Medium
xyx = 2

Let f(x) = (4x + 3)3. Find f′(2).

f(x) = (4x + 3)3x = 2
f′(2) =
5.Hard
xyx = 2

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

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

Let f(x) = x3 − 9x2 + 24x − 5. Find the x-coordinate x of the local maximum.

f(x) = x3 − 9x2 + 24x − 5
x =

Answer key

  1. 1. f′(3) = −487
  2. 2. f′(−3) = −1664
  3. 3. f′(0.5) = 1.382
  4. 4. f′(2) = 1452
  5. 5. b = 6
  6. 6. x = 2

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