Answer
$f'(x) = x^{2} g'(x) + 2x g(x)$
Work Step by Step
$f(x) = x^{2} g(x)$
Use chain rule here
$f'(x) = x^{2} \frac{d}{dx}g (x) + g(x) \frac{d}{dx} x^{2} $
$f'(x) = x^{2} g'(x) + 2x g(x)$
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