JUPEBMathematicsDifferentiation

Differentiate $y = x^2 e^x$ with respect to $x$.

A$x e^x (x + 2)$CORRECT
B$2x e^{x-1}$
C$2x e^x$
D$x^2 e^x$
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Why the answer is A, and why the others tempt you.
Apply the product rule $\dfrac{d}{dx}(uv) = u'v + uv'$ with $u = x^2$ and $v = e^x$: $2x e^x + x^2 e^x = x e^x (2 + x)$. Differentiating only the $x^2$ factor gives $2x e^x$, which is incomplete.
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