Can you give an example of a function [itex]f:X\times Y\to\mathbb{R}[/itex], where [itex]X,Y\subset\mathbb{R}[/itex], such that the integral(adsbygoogle = window.adsbygoogle || []).push({});

[tex]

\int\limits_Y f(x,y) dy

[/tex]

converges for all [itex]x\in X[/itex], the partial derivative

[tex]

\partial_x f(x,y)

[/tex]

exists for all [itex](x,y)\in X\times Y[/itex], and the integral

[tex]

\int\limits_Y \partial_x f(x,y) dy

[/tex]

diverges at least for some [itex]x\in X[/itex]?

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# Example of non-integrable partial derivative

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