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AP® Calculus AB-BC

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Difficult

Fractions Inside the Radical: Chain Rule

APCALC-YFLNDY

If $ f ( x )=\sqrt{\cfrac{x+1}{2x-1}} $, find $f^\prime(x)$.

A

$\cfrac{1}{2} \cdot \cfrac{1}{(x+1)(2x-1)} \sqrt {\cfrac{x+1}{2x-1}}$

B

$ \cfrac{1}{4} \sqrt { \cfrac{x+1}{2x-1}} $

C

$ \cfrac{-3}{2 ( x+1 ) ( 2x-1 )} \cdot \sqrt { \cfrac{x+1}{2x-1}} $

D

$- \cfrac{3}{{2{{(2x - 1)}^2}}} \cdot \sqrt {\cfrac{{x + 1}}{{2x - 1}}} $