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## Main Question or Discussion Point

I remember before reading bits and pieces about how if we have a function of two variables, say f = f(x,y), then it must be true that d/dx(df/dy) = d/dy(df/dx), where the "d"'s are partials.

Can anyone guide me to what this theorem is called or to its implications? Also, does it work in reverse? i.e. if it is true that d/dx(df/dy) = d/dy(df/dx) for some function f, then does f necessarily exist?

Can anyone guide me to what this theorem is called or to its implications? Also, does it work in reverse? i.e. if it is true that d/dx(df/dy) = d/dy(df/dx) for some function f, then does f necessarily exist?