AP Calculus ABmediummcq1 pt
If f(x) = (x² + 1)/(x - 1), then f'(x) =
A.(2x(x - 1) - (x² + 1))/(x - 1)^2
B.(2x(x - 1) + (x² + 1))/(x - 1)^2
C.(2x)/(x - 1)
D.(x² + 1)/(x - 1)^2
Explanation
Core Concept
This requires the quotient rule: (u/v)' = (u'v - uv')/v². Here u = x² + 1, u' = 2x, v = x - 1, v' = 1. So f'(x) = (2x(x - 1) - (x² + 1))/(x - 1)^2.
Correct Answer
A(2x(x - 1) - (x² + 1))/(x - 1)^2
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