Resubmitting this question because the last answer I received was completely unhelpful and incomplete.

Resubmitting this question because the last answer I received was completely unhelpful and incomplete. I need help with computing the following in multivariable terms with Df(a) being a derivative in the sense of a linear transformation.

Consider f : R2 → R, given by f (x,y) = (xy)^1/3 Determine for which a ∈ R2 the partial derivatives fx(a) and fy(a) exist.

Main part: For which a does Df(a) exist?