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