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 + 3x2 + 9x + 9. Find the slope of the graph at x = 2, that is f′(2).

f(x) = −5x4 + 3x2 + 9x + 9x = 2
f′(2) =
2.Easy
xyx = 3

Let f(x) = 5x4 + 6x2 + 5x − 8. Find the slope of the graph at x = 3, that is f′(3).

f(x) = 5x4 + 6x2 + 5x − 8x = 3
f′(3) =
3.Medium
xyx = −1

Let f(x) = ln(x2 + 4). Find f′(−1).

f(x) = ln(x2 + 4)x = −1
f′(−1) =
4.Medium
xyx = 1

Let f(x) = ln(2x2 + 5). Find f′(1).

f(x) = ln(2x2 + 5)x = 1
f′(1) =
5.Hard
xyx = 2

The tangent line to f(x) = 0.5x2 − 2x + 3 at x = 2 crosses the y-axis at y = b. Find b.

f(x) = 0.5x2 − 2x + 3x = 2
b =
6.Hard
xy

Let f(x) = x3 + 1.5x2 + 5. Find the x-coordinate x of the local maximum.

f(x) = x3 + 1.5x2 + 5
x =

Answer key

  1. 1. f′(2) = −139
  2. 2. f′(3) = 581
  3. 3. f′(−1) = −0.4
  4. 4. f′(1) = 0.5714
  5. 5. b = 1
  6. 6. x = −1

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