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Where [tex]\phi = \phi(x)[/tex] and the functional [tex]F=F(\phi(x)) = \int d^d x [\frac{1}{2}K^2(\bigtriangledown\phi)^2+ V (\phi)][/tex]

, the author says the derivative with respect to phi gives

[tex]\frac {\partial F} {\partial \phi(x)} = -K^2\bigtriangledown^2\phi + V'(\phi)[/tex]

I'm not seeing this. Could anyone give me some tips for writing down the differentiation more explicitly? I'm trying to work it out by writing F(phi+ dphi) and subtracting F(phi) as detailed in http://julian.tau.ac.il/bqs/functionals/node1.html, but I can't seem to make it come out correctly. This is the chemical potential in the Cahn-Hilliard equation, if it's important.

Thanks in advance!

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# Differentiation of an integral

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