If I had a function g(x) defined by(adsbygoogle = window.adsbygoogle || []).push({});

[tex]g(x) = \int_{-\infty}^{\infty} f(x) \delta(x) dx[/tex]

where [tex]\delta(x)[/tex] is the dirac delta function, what would dg(x)/dx be? The fundamental theorem of calculus requires that [tex]f(x) \delta(x)[/tex] needs to be a continuous and differentiable function before I can immediately say that dg(x)/dx = f(x) \delta(x), which is clearly not the case.

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# Derivative of an integral containing a Dirac delta

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