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

f(x) = 2x4 + x2 − 4x = −3
f′(−3) =
2.Easy
xyx = −2

Let f(x) = −5x5 − 9x2 − 2x + 2. Find the slope of the graph at x = −2, that is f′(−2).

f(x) = −5x5 − 9x2 − 2x + 2x = −2
f′(−2) =
3.Medium
xyx = 1.5

Let f(x) = x·sin(2x), with x in radians. Find f′(1.5).

f(x) = x·sin(2x)x = 1.5 rad
f′(1.5) =
4.Medium
xyx = −2

Let f(x) = ln(3x2 + 2). Find f′(−2).

f(x) = ln(3x2 + 2)x = −2
f′(−2) =
5.Hard
xyx = −2

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

f(x) = x2 − 4x = −2
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) = −222
  2. 2. f′(−2) = −366
  3. 3. f′(1.5) = −2.829
  4. 4. f′(−2) = −0.8571
  5. 5. b = −8
  6. 6. b = 0.5

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