# Functional Derivative

1. Jul 1, 2011

### Derivator

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 $\lambda$, that is $F[f(x,\lambda)]$ then:
$$\frac{\partial F}{\partial \lambda} = \int \frac{\delta F}{\delta f(x)} \frac{\partial f(x)}{\partial \lambda} dx$$

Does anyone know a rigorous proof? (What bothers me a bit is the mixed appearance of the partial derivative $\partial$ and the functional derivative $\delta$)