  We prove that for every function $f:X\to Y$, where $X$ is a separable Banach
space and $Y$ is a Banach space with RNP, there exists a set $A\in\tilde\mcA$
such that $f$ is Gateaux differentiable at all $x\in S(f)\setminus A$, where
$S(f)$ is the set of points where $f$ is pointwise-Lipschitz. This improves a
result of Bongiorno. As a corollary, we obtain that every $K$-monotone function
on a separable Banach space is Hadamard differentiable outside of a set
belonging to $\tilde\mcC$; this improves a result due to Borwein and Wang.
Another corollary is that if $X$ is Asplund, $f:X\to\R$ cone monotone,
$g:X\to\R$ continuous convex, then there exists a point in $X$, where $f$ is
Hadamard differentiable and $g$ is Frechet differentiable.
