\begin{definition}[Definition:Left-Hand Derivative/Real Function]
Let $f: \R \to \R$ be a real function.
The '''left-hand derivative''' of $f$ is defined as the left-hand limit:
:$\ds \map {f'_-} x = \lim_{h \mathop \to 0^-} \frac {\map f {x + h} - \map f x} h$
If the '''left-hand derivative''' exists, then $f$ is said to be '''left-hand differentiable''' at $x$.
\end{definition}