\begin{definition}[Definition:Right-Hand Derivative]
Let $B$ be a Banach space over the set of real numbers $\R$.
Let $f: \R \to B$ be a mapping from $\R$ to $B$.
The '''right-hand derivative''' of $f$ is defined as the right-hand limit:
:$\ds \map {f'_+} x = \lim_{h \mathop \to 0^+} \frac {\map f {x + h} - \map f x} h$
If the '''right-hand derivative''' exists, then $f$ is said to be '''right-hand differentiable''' at $x$.
\end{definition}