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AP® Calculus AB-BC

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Moderate

Derivative Using Logarithmic Properties

APCALC-JDMFXK

Given the following function:

$$y=\ln { ( \cfrac { \sqrt { x-1 } }{ 4x-5 } ) } $$

...find $\cfrac{dy}{dx}$.

A

$ \cfrac{1}{\sqrt{x-1}}-\cfrac{1}{4x-5} $

B

$ \cfrac{1}{\sqrt{x-1}}-\cfrac{4}{4x-5} $

C

$ \cfrac{4x-5}{\sqrt{x-1}} $

D

$\cfrac{1}{2 ( x-1 )}-\cfrac{4}{4x-5}$

E

$ \cfrac{ ( 4x-5 ) ( 4x-3 )}{ ( 2 ( x-1 )^{2} )} $