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It looks like it comes from the total derivative but I can not understand their notation so I can not derive it.
Hmm. I think maybe that comes from an illustration.
As part of the proof, they are saying that
is the total differential of the function f(x,y). Why?
Thanks. I am particularly confused by the minus sign.
Yes, I agree. It was useful for solving the ODEs we were given in class when we had to differentiate annoying functions twice and sub initial conditions, etc... do you remember how it is derived?
I came across an interesting tool which would help for differentiating functions involving x and y;
where f is a function of x and y and the deltas denote partial derivatives.
But why is this the case?