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) = −3x5 − 4x2 − 4x − 2. Find the slope of the graph at x = −3, that is f′(−3).

f(x) = −3x5 − 4x2 − 4x − 2x = −3
f′(−3) =
2.Easy
xyx = −2

Let f(x) = −3x5 − x2 + 5x + 5. Find the slope of the graph at x = −2, that is f′(−2).

f(x) = −3x5 − x2 + 5x + 5x = −2
f′(−2) =
3.Medium
xyx = 1

Let f(x) = x3·e0.5x. Find f′(1).

f(x) = x3·e0.5xx = 1
f′(1) =
4.Medium
xyx = 2

Let f(x) = x·sin(3x), with x in radians. Find f′(2).

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

The tangent line to f(x) = 3x2 − 5 at x = −2 crosses the y-axis at y = b. Find b.

f(x) = 3x2 − 5x = −2
b =
6.Hard
xy

Let f(x) = x3 − 12x2 + 45x + 6. Find the x-coordinate x of the local maximum.

f(x) = x3 − 12x2 + 45x + 6
x =

Answer key

  1. 1. f′(−3) = −1195
  2. 2. f′(−2) = −231
  3. 3. f′(1) = 5.771
  4. 4. f′(2) = 5.482
  5. 5. b = −17
  6. 6. x = 3

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