Definition:Left-Hand Derivative/Real Function

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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 $x$.

Also known as

Some sources give this as the left derivative.

Some refer to it as the derivative on the left.

Also see