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) = −4x4 + 8x2 + 9x. Find the slope of the graph at x = −2, that is f′(−2).

f(x) = −4x4 + 8x2 + 9xx = −2
f′(−2) =
2.Easy
xyx = 1

Let f(x) = −x5 + 6x2 + 4x − 1. Find the slope of the graph at x = 1, that is f′(1).

f(x) = −x5 + 6x2 + 4x − 1x = 1
f′(1) =
3.Medium
xyx = 0.5

Let f(x) = x·e0.5x. Find f′(0.5).

f(x) = x·e0.5xx = 0.5
f′(0.5) =
4.Medium
xyx = 2

Let f(x) = (3x + 1)4. Find f′(2).

f(x) = (3x + 1)4x = 2
f′(2) =
5.Hard
xy

Let f(x) = x3 − 13.5x2 + 54x. Find the x-coordinate x of the local maximum.

f(x) = x3 − 13.5x2 + 54x
x =
6.Hard
xyx = 1

The tangent line to f(x) = 2x2 + 4x + 1 at x = 1 crosses the y-axis at y = b. Find b.

f(x) = 2x2 + 4x + 1x = 1
b =

Answer key

  1. 1. f′(−2) = 105
  2. 2. f′(1) = 11
  3. 3. f′(0.5) = 1.605
  4. 4. f′(2) = 4116
  5. 5. x = 3
  6. 6. b = −1

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