Proof of derivation of the chain rule (compound function derivation)
This article gives two proof methods, the first is advanced mathematics (complex), and the second is Wikipedia (simple)One: The proof given by the advanced mathematics textbook of Tongji University:
Two: Proof from Wikipedia
A simple proof is given below:
Suppose the function sum
, where x is an independent variable, f(g(x)) is derivable at g(x), and g(x) is derivable at x.
According to the definition of derivable:
which 
at that time
(Here is the increment Δx mentioned in the advanced mathematics book)
In the same way:
When 
_
Now
in:
Noticed at the time . 
and 
therefore 
therefore
Prove it.
Reference material: Tongji University Advanced Mathematics Textbook Sixth Edition Volume 1
Wikipedia: Wikipedia: https://zh.wikipedia.org/wiki/é¾å¼æ³åå