This is supposedly the chain rule with functional derivative:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]

\frac{\delta F}{\delta\psi(x)} = \int dy\; \frac{\delta F}{\delta\phi(y)}\frac{\delta\phi(y)}{\delta\psi(x)}

[/tex]

I have difficulty understanding what everything in this identity means. The functional derivative is usually a derivative of a functional with respect to some function, like in the term

[tex]

\frac{\delta F}{\delta\phi(y)} := \lim_{\epsilon\to 0} \frac{1}{\epsilon}\big( F(\phi + \epsilon \delta_y) - F(\phi)\big),

[/tex]

but isn't the term

[tex]

\frac{\delta\phi(y)}{\delta\psi(x)} := ?

[/tex]

now a derivative of a function with respect to another function?

**Physics Forums - The Fusion of Science and Community**

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!

# Chain rule with functional derivative

Loading...

Similar Threads - Chain rule functional | Date |
---|---|

I Rigorously understanding chain rule for sum of functions | Aug 6, 2017 |

I Heavyside step function chain rule | Mar 21, 2017 |

I Applying Chain Rule to a function of two variables | Dec 9, 2016 |

I Integration - chain rule / functional | Oct 19, 2016 |

I Chain rule in a multi-variable function | May 7, 2016 |

**Physics Forums - The Fusion of Science and Community**