In general, given a function $f\left(x_{1},\dots,x_{n}\right)$ and functions $f_{1}\left(x_{1},\dots,x_{n}\right)$, $\dots$, $f_{n}\left(x_{1},\dots,x_{n}\right)$, is there a rule to find the partial derivative of $f\left(f_{1}\left(x_{1},\dots,x_{n}\right),\dots,f_{n}\left(x_{1},\dots,x_{n}\right)\right)$ with respect to $x_{i}$?
2026-03-31 21:53:11.1774993991
Derivative of $f\left(f_{1}\left(x_{1},\dots,x_{n}\right),\dots,f_{n}\left(x_{1},\dots,x_{n}\right)\right)$ with respect to $x_{i}$
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