Category:Examples of Distributional Derivatives

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This category contains examples of 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:

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