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Given $y=\cfrac{2^{ -2x }}{{ e }^{ -2x }},$ find $\cfrac{dy}{dx}$.

A

${ 2e }^{ 2x }\left( \cfrac{1}{2} \right)^{ 2x }( 1-\ln2 ) $

B

${ e }^{ 2x }( 1-\ln2 ) $

C

${ 2e }^{ 2x }\left( \cfrac{1}{2} \right) ^{ 2x }$

D

${ 2e }^{ 2x }\left( \cfrac{1}{2} \right) ^{ 2x }\ln { 2 } $

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