  The classical Denjoy-Young-Saks theorem on Dini derivatives of arbitrary
functions $f: \R \to \R$ was extended by U.S. Haslam-Jones (1932) and A.J. Ward
(1935) to arbitrary functions on $\R^2$. This extension gives the strongest
relation among upper and lower Hadamard directional derivatives $f^+_H (x,v)$,
$f^-_H (x,v)$ ($v \in X$) which holds almost everywhere for an arbitrary
function $f:\R^2\to \R$. Our main result extends the theorem of Haslam-Jones
and Ward to functions on separable Banach spaces.
