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AP® Calculus AB-BC

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Difficult

Nested Log Functions

APCALC-LQ4WGH

What is the derivative of $f( x ) =\ln\left(\cfrac{\ln x}{x } \right) , $ with respect to ‘$x$’?

A

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

B

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

C

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

D

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