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AP® Calculus AB-BC

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Moderate

Power Rule Challenge: Fractions in the Exponent

APCALC-RJLNFL

What is the derivative of $f( x ) ={ x }^{\frac{1}{3}}( { x }^{\frac{3}{5}}+{ x }^{ \frac{1}{2}} )$ with respect to $x$?

A

$f^{ \prime }( x ) =\cfrac {14x ^{ \frac {1}{15}}}{15}+ \cfrac {5x ^{ \frac {1}{6}}}{6}$

B

$f^{ \prime }( x ) =15x^{ \frac {14}{15}}+6x^{ \frac {5}{6}}$

C

$f^{ \prime }( x ) =\cfrac{14}{ 15x^{ \frac {1}{15}}}+\cfrac{5}{ 6x^{\frac{1}{6}}} $

D

$f^{ \prime }( x ) = \cfrac {1}{5 x ^{ \frac {4}{5}}}+ \cfrac {1}{6x ^{ \frac {5}{6}}}$