Definition 18.3.1 (Right-Differentiable). Let $-\infty < a < b < \infty$, $E$ be a separated topological vector space, $f: [a, b] \to E$, and $x \in [a, b)$, then $f$ is right-differentiable at $x$ if
\[D^{+}f(x) = \lim_{t \downto 0}\frac{f(x + t) - f(x)}{t}\]
exists.