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 − 9x2 − 8x + 7. Find the slope of the graph at x = −3, that is f′(−3).

f(x) = 4x3 − 9x2 − 8x + 7x = −3
f′(−3) =
2.Easy
xyx = −2

Let f(x) = 2x4 + 8x2 − 6. Find the slope of the graph at x = −2, that is f′(−2).

f(x) = 2x4 + 8x2 − 6x = −2
f′(−2) =
3.Medium
xyx = 2

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

f(x) = x·sin(x)x = 2 rad
f′(2) =
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 = 3

The tangent line to f(x) = 0.5x2 + 5x at x = 3 crosses the y-axis at y = b. Find b.

f(x) = 0.5x2 + 5xx = 3
b =
6.Hard
xyx = 1

The tangent line to f(x) = 0.5x2 + 2x + 1 at x = 1 crosses the y-axis at y = b. Find b.

f(x) = 0.5x2 + 2x + 1x = 1
b =

Answer key

  1. 1. f′(−3) = 154
  2. 2. f′(−2) = −96
  3. 3. f′(2) = 0.077
  4. 4. f′(2) = 5.482
  5. 5. b = −4.5
  6. 6. b = 0.5

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