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) = −5x3 + 8x2 − 4x + 3. Find the slope of the graph at x = 3, that is f′(3).

f(x) = −5x3 + 8x2 − 4x + 3x = 3
f′(3) =
2.Easy
xyx = −1

Let f(x) = −3x4 − 7x2 − 3x + 4. Find the slope of the graph at x = −1, that is f′(−1).

f(x) = −3x4 − 7x2 − 3x + 4x = −1
f′(−1) =
3.Medium
xyx = 2

Let f(x) = x·sin(2x), with x in radians. Find f′(2).

f(x) = x·sin(2x)x = 2 rad
f′(2) =
4.Medium
xyx = −1

Let f(x) = ln(x2 + 1). Find f′(−1).

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

The tangent line to f(x) = 3x2 − x − 4 at x = −2 crosses the y-axis at y = b. Find b.

f(x) = 3x2 − x − 4x = −2
b =
6.Hard
xy

Let f(x) = x3 − 13.5x2 + 54x − 2. Find the x-coordinate x of the local maximum.

f(x) = x3 − 13.5x2 + 54x − 2
x =

Answer key

  1. 1. f′(3) = −91
  2. 2. f′(−1) = 23
  3. 3. f′(2) = −3.371
  4. 4. f′(−1) = −1
  5. 5. b = −16
  6. 6. x = 3

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