  We characterize the limited operators by differentiability of convex
continuous functions. Given Banach spaces $Y$ and $X$ and a linear continuous
operator $T: Y \longrightarrow X$, we prove that $T$ is a limited operator if
and only if, for every convex continuous function $f: X \longrightarrow \R$ and
every point $y\in Y$, $f\circ T$ is Fr\'echet differentiable at $y\in Y$
whenever $f$ is G\^ateaux differentiable at $T(y)\in X$.
