Just a quick question... I have two functions – $V(a,b,c)$ and $F(a,b,c)$ – and I wish to calculate the derivative of one with respect to another ($\frac{\partial V}{\partial F}$). Am I right in thinking that this is a functional derivative, and must be calculated using something like:
$\frac{\delta V}{\delta F} = \frac{\partial v}{\partial F} - \nabla \cdot \frac{\partial v}{\partial \nabla F}$
Rather than just an application of the chain rule:
$\frac{\partial V}{\partial F} = \frac{\partial V}{\partial a}\frac{\partial a}{\partial F} + \frac{\partial V}{\partial b}\frac{\partial b}{\partial F} + \frac{\partial V}{\partial c}\frac{\partial c}{\partial F}$
I'm not that familiar with functional derivatives – would someone be able to point me to a straightforward practical example of a functional derivative calculation, if that is indeed required?
Much appreciated :)