# Definition:Left-Hand Derivative/Real Function

## Definition

Let $f: \R \to B$ be a real function.

The left-hand derivative of $f$ is defined as the left-hand limit:

$\displaystyle f'_- \left({x}\right) = \lim_{h \mathop \to 0^-} \frac {f \left({x + h}\right) - f \left({x}\right)} h$

If the left-hand derivative exists, then $f$ is said to be left-hand differentiable at $x$.