= Differentiation commutes with convolution
{title2=$D^\alpha(T*\phi)=(D^\alpha T)*\phi=T*(D^\alpha\phi)$}
= Convolution derivative identity
{synonym}
For a <distribution> and a compactly supported smooth kernel, differentiation with constant coefficients commutes with <convolution> wherever the kernel support stays inside the domain. The identity follows by testing against the translated kernel and tracking the sign of its derivative. A variable coefficient must remain inside the product before <convolution>; in general $(bu)_\sigma\ne bu_\sigma$.
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