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 − 9x2 − 2x − 3. Find the slope of the graph at x = 3, that is f′(3).

f(x) = 5x3 − 9x2 − 2x − 3x = 3
f′(3) =
2.Easy
xyx = −3

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

f(x) = 3x5 − 9x2 − 8x − 3x = −3
f′(−3) =
3.Medium
xyx = 1.5

Let f(x) = x·sin(3x), with x in radians. Find f′(1.5).

f(x) = x·sin(3x)x = 1.5 rad
f′(1.5) =
4.Medium
xyx = 0

Let f(x) = (3x + 3)3. Find f′(0).

f(x) = (3x + 3)3x = 0
f′(0) =
5.Hard
xyx = 2

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

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

Let f(x) = x3 − 10.5x2 + 36x − 5. Find the x-coordinate x of the local minimum.

f(x) = x3 − 10.5x2 + 36x − 5
x =

Answer key

  1. 1. f′(3) = 79
  2. 2. f′(−3) = 1261
  3. 3. f′(1.5) = −1.926
  4. 4. f′(0) = 81
  5. 5. b = −14
  6. 6. x = 4

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