Definition:Right-Hand Derivative/Real Function

Definition

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

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 $x$.

Also known as

Some sources give this as the right derivative.

Some refer to it as the derivative on the right.