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                <term xml:lang="en">Gâteaux-differentiability</term>
                <term xml:lang="en">Fréchet-differentiability</term>
                <term xml:lang="en">convex functions and extreme points</term>
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              <p>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 $T(y)\in X$.</p>
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