Definition:Distributional Derivative

Definition
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:


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