Differential of map from surface to surface

[EV33]

Homework Statement

Does anyone know the process for finding the differential of of f:S→S' where S,S' are surfaces.

My textbook explains how to do this when f is a vector valued function but in the problem that I am working on I have something like f(x,y)=(g(x),h(x),j(y)) rather than something like this f(t)=(g(t),h(t),j(t)).

Thank you.

 

[EV33]

Never Mind. I figured it out.