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