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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

    [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]
     
  2. jcsd
  3. Jan 20, 2007 #2
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