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) = 4x4 + 2x2 − 3x − 5. Find the slope of the graph at x = −3, that is f′(−3).

f(x) = 4x4 + 2x2 − 3x − 5x = −3
f′(−3) =
2.Easy
xyx = 1

Let f(x) = 4x3 − 9x2 + 9x + 6. Find the slope of the graph at x = 1, that is f′(1).

f(x) = 4x3 − 9x2 + 9x + 6x = 1
f′(1) =
3.Medium
xyx = −1

Let f(x) = ln(3x2 + 1). Find f′(−1).

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

Let f(x) = ln(x2 + 2). Find f′(2).

f(x) = ln(x2 + 2)x = 2
f′(2) =
5.Hard
xyx = 3

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

f(x) = 3x2 − 2x = 3
b =
6.Hard
xy

Let f(x) = x3 + 3x2 + 6. Find the x-coordinate x of the local maximum.

f(x) = x3 + 3x2 + 6
x =

Answer key

  1. 1. f′(−3) = −447
  2. 2. f′(1) = 3
  3. 3. f′(−1) = −1.5
  4. 4. f′(2) = 0.6667
  5. 5. b = −29
  6. 6. x = −2

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