Definition:Right-Hand Derivative
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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:
- $\ds \map {f'_+} x = \lim_{h \mathop \to 0^+} \frac {\map f {x + h} - \map f x} h$
If the right-hand derivative exists, then $f$ is said to be right-hand differentiable at $x$.
Real Functions
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.