If I understand the parent comment correctly, this is the advanced version of "proofs" of propositions in economics that just assume that dy/dx is defined in su

If I understand the parent comment correctly, this is the advanced version of "proofs" of propositions in economics that just assume that dy/dx is defined in such a way that dy/dz = (dy/dx)(dx/dz). A mathematician would say "Let y: U\to V where U,V are open subsets of R^k and y\in C^1 (or C^\infty). Then..." and define clearly what's a function, what's a variable/number/vector and so forth.