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) = 4x3 + 2x2 − x − 5. Find the slope of the graph at x = −3, that is f′(−3).

f(x) = 4x3 + 2x2 − x − 5x = −3
f′(−3) =
2.Easy
xyx = −1

Let f(x) = 5x3 + 6x2 + 5x + 7. Find the slope of the graph at x = −1, that is f′(−1).

f(x) = 5x3 + 6x2 + 5x + 7x = −1
f′(−1) =
3.Medium
xyx = 1.5

Let f(x) = x·sin(x), with x in radians. Find f′(1.5).

f(x) = x·sin(x)x = 1.5 rad
f′(1.5) =
4.Medium
xyx = 1

Let f(x) = ln(3x2 + 1). Find f′(1).

f(x) = ln(3x2 + 1)x = 1
f′(1) =
5.Hard
xy

Let f(x) = x3 + 6x2 + 9x. Find the x-coordinate x of the local maximum.

f(x) = x3 + 6x2 + 9x
x =
6.Hard
xyx = −1

The tangent line to f(x) = 2x2 + 5x + 1 at x = −1 crosses the y-axis at y = b. Find b.

f(x) = 2x2 + 5x + 1x = −1
b =

Answer key

  1. 1. f′(−3) = 95
  2. 2. f′(−1) = 8
  3. 3. f′(1.5) = 1.104
  4. 4. f′(1) = 1.5
  5. 5. x = −3
  6. 6. b = −1

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