On differentiability of functions of two variables (Q1978893)

The authors introduce a notion of a family of equidifferentiable functions to establish some sufficient conditions for the differentiability of functions \(F:\mathbb R^2\to \mathbb R\) in terms of the sections \(F_x(t):=F(x,t)\) and \(F^y(t):=F(t,y)\). It is also discussed whether some other properties of the sections \(F_x\) and \(F^y\) imply (or not) the differentiability of the function \(F\). The proved results are illustrated by nontrivial examples.