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AP® Calculus AB-BC

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Moderate

Derivative Of An Inverse

APCALC-YJ0ULN

Given: $g$ and $f$ are differentiable functions and $g( x ) =f^{ -1 }( x ) .$

If $g( 5 ) =1, f( 1 ) =5, f^{ \prime }( 1 ) =3$ and $f^{ \prime }( 5 ) =6$, find $g^\prime(5)$.

A

$1$

B

$\cfrac{1}{3}$

C

$-3$

D

$\cfrac{1}{6}$