Definition:Derivative of Tempered Distribution

Definition
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:


 * $\map {\dfrac {\d T} {\d x}} \phi := - \map T {\dfrac {\d \phi} {\d x}}$