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AP® Calculus AB-BC

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Derivative Of Arccot(3x)

APCALC-BLTE1F

Given the function $\DeclareMathOperator{\arccot}{arccot} f( x ) =\arccot { ( 3x ) } ,$ find $f^\prime(x)$.

A

$\cfrac{1}{\sqrt{( 1+{ 9x }^{ 2 } ) }}$

B

$\cfrac{-1}{\sqrt{( 1+{ 9x }^{ 2 } ) }}$

C

$\cfrac{-3}{( 1+{ 9x }^{ 2 } ) }$

D

$\cfrac{3}{\sqrt{( 1+{ 9x }^{ 2 } ) }}$