Total Differentiation with Nested, Unspecified Composite Functions
I have no idea if the thread title accurately explains the question I'm having, but it is the best I could do. Googled and searched the forum and couldn't find what I was looking for.
Basically, I'm familiar with total differentiation. For instance I'm fairly certain that for a function
the total derivative is
But what if the composite functions are functions of many variables. For instance,
My first attempt for the total differential w.r.t. :
My second attempt:
Are either correct? Any help is appreciated!