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) = −2x4 − 6x2 + 5x − 5. Find the slope of the graph at x = 3, that is f′(3).

f(x) = −2x4 − 6x2 + 5x − 5x = 3
f′(3) =
2.Easy
xyx = −2

Let f(x) = −5x3 + 4x2 + 7x + 8. Find the slope of the graph at x = −2, that is f′(−2).

f(x) = −5x3 + 4x2 + 7x + 8x = −2
f′(−2) =
3.Medium
xyx = 2

Let f(x) = (−2x + 3)3. Find f′(2).

f(x) = (−2x + 3)3x = 2
f′(2) =
4.Medium
xyx = 2

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

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

Let f(x) = x3 − 12x2 + 45x − 6. Find the x-coordinate x of the local maximum.

f(x) = x3 − 12x2 + 45x − 6
x =
6.Hard
xyx = −1

The tangent line to f(x) = 0.5x2 + x + 5 at x = −1 crosses the y-axis at y = b. Find b.

f(x) = 0.5x2 + x + 5x = −1
b =

Answer key

  1. 1. f′(3) = −247
  2. 2. f′(−2) = −69
  3. 3. f′(2) = −6
  4. 4. f′(2) = −3.371
  5. 5. x = 3
  6. 6. b = 4.5

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