# Definition:Right-Hand Derivative

## Definition

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:

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

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

### Real Functions

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

The right-hand derivative of $f$ is defined as the right-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 right-hand derivative exists, then $f$ is said to be right-hand differentiable at $x$.