Question

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Answer 1

Answer:

$(2) \: is \: correct \: option$

Explanation:

$\frac{d}{dx} ( \frac{ {y}^{2} }{2} ) = \frac{1}{2} ( \frac{d(y {}^{2}) }{dx} )$

$\frac{d}{dx} ( \frac{ {y}^{2} }{2} ) = ( {x}^{2} {e}^{x} )(2x {e}^{x} + x {}^{2} {e}^{x})$

$= x ^{3} {e}^{2x} (2 + x)$