\begin{definition}[Definition:Distributional Partial Derivative]
Let $d \in \N$.
Let $\phi \in \map \DD {\R^d}$ be a test function.
Let $T \in \map {\DD'} {\R^d}$ be a distribution.
Let $i \in \N : 1 \le i \le d$.
The '''distributional partial derivative''' $\ds \dfrac {\partial T} {\partial x_i} \in \map {\DD'} {\R^d}$ is defined by:
:$\map {\dfrac {\partial T} {\partial x_i}} \phi := - \map T {\dfrac {\partial \phi} {\partial x_i}}$
\end{definition}