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) = −4x5 − 8x2 + 9x + 6. Find the slope of the graph at x = −3, that is f′(−3).

f(x) = −4x5 − 8x2 + 9x + 6x = −3
f′(−3) =
2.Easy
xyx = −1

Let f(x) = 5x4 + x2 + 8x + 1. Find the slope of the graph at x = −1, that is f′(−1).

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

Let f(x) = ln(x2 + 1). Find f′(3).

f(x) = ln(x2 + 1)x = 3
f′(3) =
4.Medium
xyx = 2

Let f(x) = (3x − 3)3. Find f′(2).

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

The tangent line to f(x) = 0.5x2 + 3x − 1 at x = 2 crosses the y-axis at y = b. Find b.

f(x) = 0.5x2 + 3x − 1x = 2
b =
6.Hard
xy

Let f(x) = x3 + 10.5x2 + 36x + 4. Find the x-coordinate x of the local minimum.

f(x) = x3 + 10.5x2 + 36x + 4
x =

Answer key

  1. 1. f′(−3) = −1563
  2. 2. f′(−1) = −14
  3. 3. f′(3) = 0.6
  4. 4. f′(2) = 81
  5. 5. b = −3
  6. 6. x = −3

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