Assume that \(u \in C_{c}\left(\mathbb{R}^{n}ight)\) and \(w \in C^{\infty}\left(\mathbb{R}^{n}ight)\). Show that \(u \star w\) exists, is of class \(C^{\infty}\) and satisfies

\[\frac{\partial}{\partial x_{i}}(u \star w)=u \star\left(\frac{\partial}{\partial x_{i}} wight)\]