I have been studying partial derivatives and I came across the chain rule for multi-variable functions. I have attached the definition I was given below, and I need help making sense of it.
I understand that if we have n variables and each of those variables is a function of m variables, but what happens in the case when each of those variables is NOT a function of m variables.
For example, when differentiating F(x, y, f(x, y))= 0, only z is a function of x and y and the variables x and y themselves are not.
Can someone point me in the right direction and explain to me what I am missing or not understanding? Could the definition be worded in such a way to say that each variable needs to be a function of at least 1 of the m variables?
