While studying weak derivatives I've searched for examples of these functions (compact support and $C^{\infty}$), but all I've found look like this one: $$ f(x)=\left\{ \begin{array}{lcc} e^{\frac{-1}{1-x^2}} & |x|<1 \\ \\ 0 & |x|\geq 1 \\ \end{array} \right. $$
Could someone give another example?