[问答题]
Let $y=x^{2} e^{x}$ , for $x \in \mathbb{R}$ .
1. Find $frac{\mathrm{d} y}{\mathrm{~d} x}$ .
2. Prove by mathematical induction that
$\frac{\mathrm{d}^{n}}{\mathrm{~d} x^{n}}\left(x^{2} e^{x}\right)=\left(n(n-1)+2 n x+x^{2}\right) e^{x} \quad \text { for all } n \in \mathbb{Z}^{+}, n \geq 2$
