Derivator
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Hi,
in their book ''Density-Functional Theory of Atoms and Molecules'' Parr and Yang state in Appendix A, Formula (A.33)
If F ist a functional that depends on a parameter [itex]\lambda[/itex], that is [itex]F[f(x,\lambda)][/itex] then:
[tex]\frac{\partial F}{\partial \lambda} = \int \frac{\delta F}{\delta f(x)} \frac{\partial f(x)}{\partial \lambda} dx[/tex]
Does anyone know a rigorous proof? (What bothers me a bit is the mixed appearance of the partial derivative [itex]\partial[/itex] and the functional derivative [itex]\delta[/itex])
in their book ''Density-Functional Theory of Atoms and Molecules'' Parr and Yang state in Appendix A, Formula (A.33)
If F ist a functional that depends on a parameter [itex]\lambda[/itex], that is [itex]F[f(x,\lambda)][/itex] then:
[tex]\frac{\partial F}{\partial \lambda} = \int \frac{\delta F}{\delta f(x)} \frac{\partial f(x)}{\partial \lambda} dx[/tex]
Does anyone know a rigorous proof? (What bothers me a bit is the mixed appearance of the partial derivative [itex]\partial[/itex] and the functional derivative [itex]\delta[/itex])