I was slightly confused with some of the other posts concerning the complex version of the chain rule. It is stated as follows in other questions: $\frac{\partial h}{\partial z} = \frac{\partial g}{\partial z}\frac{\partial f}{\partial z} + \frac{\partial g}{\partial \bar z}\frac{\partial \bar f}{\partial z}$
Where h = $g\circ f$, $g:U \rightarrow \mathbb C$ and $f: V \rightarrow U$
When using the multi-variable version, The "denomiator" of the del g term is del z, whereas shouldn't be del f?
As in: $\frac{\partial h}{\partial z} = \frac{\partial g}{\partial f}\frac{\partial f}{\partial z} + \frac{\partial g}{\partial \bar f}\frac{\partial \bar f}{\partial z}$
Any insight is appreciated.
Thank you in advance!