$f$ and $g$ are functions from $D \subseteq R^n \rightarrow{R}$ and $x_0$ is in D
Let be $f$ and $g$ be differenciable at $x_0$. Prove that the product $fg$ is differentiable at $x_0$, and $d(fg)(x_0)=f(x_0)dg(x_0)+g(x_0)df(x_0)$. The hint is use the proof for $n=1$, I saw it and in a variable is to add and subtract $f (x) g (x) + h (x)$ but I don't know how to apply in several variables. Thanks