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.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Derivative of an integral containing a Dirac delta

**Physics Forums | Science Articles, Homework Help, Discussion**