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I have the following

$ \frac{d}{dn(x)} \int_{x \in \cal{R}^3} {n(x) dx} $

I know that this additional relationship holds

$ \int_{x \in \cal{R}^3}{n(x) dx} = N $

where N is a constant.

My question is, what is the value of the above derivative, and what is the procedure for this case? I am not really experienced in functionals and functional derivatives.

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    @StefanoBorini I think that $\frac{d}{dn(x)}\int_{\mathbb{R}^3}n(x)dx=\frac{dN}{dn(x)}=0$.2015-06-12

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