Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Functional derivatives

  1. Jan 20, 2007 #1
    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

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

    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

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

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

    \frac{\delta}{\delta f} =
    \frac{\delta g}{\delta f} \frac{\delta}{\delta g}?
  2. jcsd
  3. Jan 20, 2007 #2
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Functional derivatives
  1. Functional derivation (Replies: 1)

  2. Functional derivative (Replies: 1)