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AP® Calculus AB-BC

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Difficult

Concept Challenge

APCALC-KIWB5L

What is the derivative of $f( x ) =\cfrac{\ln { ( x ) }}{\sin { ( x ) }} $ with respect to $x$?

A

$f^{ \prime }( x ) =\cfrac{1}{\sin ^{ 2 }{ x }} $

B

$f^{ \prime }( x ) =\cfrac{\csc { ( x ) } +1}{\sin ^{ 2 }{ x }} $

C

$f^{ \prime }( x ) =\cfrac{\csc { (x)}}{x} -\ln { ( x ) } \cot { ( x ) } \csc { ( x ) } $

D

$f^{ \prime }( x ) =\cfrac{\cot { ( x )}}{x} +\cfrac{1}{\ln { ( x ) }} $