Let $U \subset \mathbb R^n$ be open, and let $f,g:U\to\mathbb R$ be functions with $f,g\in C^2(U)$. Then, for every $a,b\in\mathbb R$, the function $af+bg:U\to\mathbb R$ belongs to $C^2(U)$. The product function $fg:U\to\mathbb R$ belongs to $C^2(U)$. If $g(x)\ne 0$ for every $x\in U$, then the quotient function $f/g:U\to\mathbb R$ belongs to $C^2(U)$.