>>11020011Not that poster, but you can't meaningfully define the (partial) derivative in the hyperreal field because it isn't Dedekind-complete (otherwise it'd be isomorphic to R) and so the limit won't exist in general.
I add "meaningfully" because you can obviously just follow Robinson and define the derivative as the standard part of the difference quotient, but then you've just collapsed everything back into R where there's no fraction of differentials, so the inequality still holds.
