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Difficult

Product/Quotient Rule Challenge

APCALC-LIYOSZ

What is the derivative of:

$$y=\cfrac{ x \sin x}{e^x} $$

...with respect to $x$?

A

$\cfrac{dy}{dx}=-\cfrac{2( x\cos { x -\sin { x } } ) }{{ 2e }^{ x }}$

B

$\cfrac{dy}{dx}=-\cfrac{2( \sin { x + } x\sec { x -x\sin { x } } )}{{ e }^{ x }}$

C

$\cfrac{dy}{dx}=\cfrac{\sin { x } +2\cos { x } }{{ e }^{ 2x }}$

D

$\cfrac{dy}{dx}=\cfrac{ \sin { x + } x\cos { x -x\sin { x } } }{{ e }^{ x }}$