Definition:Left-Hand Derivative

Definition
Let $B$ be a Banach space over $\R$.

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

The left-hand derivative of $f$ is defined as the left-hand limit:
 * $\displaystyle f'_{-}\left({x}\right) = \lim_{h \to 0^{-}} \frac { f\left({x + h}\right) - f\left({x}\right) } {h}$

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

Also see

 * Derivative
 * Right-Hand Derivative