I'm having some trouble wrapping my mind around derivatives of a complex function of a complex variable.This is a function of two real inputs and two real outputs, correct?
What confuses me is that in multivariable calculus, the functions were of multivariable input, and had one real output. So when calculating the derivative, you'd have to know what vector you're calculating it on. In the complex space however, with two inputs and two outputs, I feel like this would also be the case? But it seems like we can use all the standard rules from single variable calc. What am I misunderstanding? Thanks!