From what theorem does this technique come from?

[omoplata]

The attached image is from "Quantum Mechanics: A self contained course" by Atkinson and Hounkonnou.

I've seen this used a lot, and I know this is simple, but I still don't know the principle behind this. From what theorem does this method come from? Can someone give me something like a Wikipedia link please?

Thanks.

 

[bp_psy]

It is the chain rule .
http://en.wikipedia.org/wiki/Chain_rule#The_chain_rule_in_higher_dimensions

 

[omoplata]

Thanks!