I was wondering. When is the following legal?(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\frac{\partial}{\partial y}\int_{-\infty}^{\+\infty}f(x,y)dx=\int_{-\infty}^{\+\infty}\frac{\partial f(x,y)}{\partial y}dx[/tex]

I know the rule when the limits of integration are bounded, but here there are four limits involved. One for the derivative, one for the integral and two for the 2 limits of integration which go to infinity and -infinity.

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# Exchanging derivative and improper integral

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