By induction it can prove Leibnitz rules
$\displaystyle D^\alpha(fg)=\sum_{|\beta| \leq |\alpha|} \binom{\alpha}{\beta} D^\beta f D^{\alpha - \beta} g$
from the book where I'm studying, it says that by Leibniz rules follows
$\displaystyle D^\alpha (fu) = f D^\alpha u + \sum_{0 < |\beta|\leq |\alpha|} C_{\beta} D^\beta f D^{\alpha -\beta} u$
where $u \in \mathcal{D}'(\Omega)$ and $f \in C^{\infty}(\Omega)$
I can not understand where it comes out this last formula, probably follow through distributional derivative?