Does there exist a chain rule for functional derivatives? For example, in ordinary univariate calculus, if we have some function [itex]y=y(x)[/itex] then the chain rule tells us (loosely) that(adsbygoogle = window.adsbygoogle || []).push({});

[tex]

\frac{d}{dy} = \frac{dx}{dy}\frac{d}{dx}.

[/tex]

Now suppose that we have a functional [itex]F[f;x)[/itex] of some function [itex]f(x)[/itex]. The functional derivative of [itex]F[f;x)[/itex] is denoted

[tex]

\frac{\delta F[f;x)}{\delta f(y)}.

[/tex]

However, suppose that [itex]f[/itex] is itself a functional of a function [itex]g(x)[/itex]. Can I then write

[tex]

\frac{\delta}{\delta f} =

\frac{\delta g}{\delta f} \frac{\delta}{\delta g}?

[/tex]

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Functional derivatives

**Physics Forums | Science Articles, Homework Help, Discussion**