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

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

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

f(x) = −x4 + 3x2 + 2x − 4x = 2
f′(2) =
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 = 0.5

Let f(x) = x·sin(2x), with x in radians. Find f′(0.5).

f(x) = x·sin(2x)x = 0.5 rad
f′(0.5) =
5.Hard
xyx = 2

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

f(x) = −x2 + x − 2x = 2
b =
6.Hard
xyx = 2

The tangent line to f(x) = 0.5x2 + 4x − 6 at x = 2 crosses the y-axis at y = b. Find b.

f(x) = 0.5x2 + 4x − 6x = 2
b =

Answer key

  1. 1. f′(3) = 51
  2. 2. f′(2) = −18
  3. 3. f′(1.5) = 1.104
  4. 4. f′(0.5) = 1.382
  5. 5. b = 2
  6. 6. b = −8

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