Definition:Left-Hand Derivative/Real Function
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Definition
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
Sources
- 1961: I.N. Sneddon: Fourier Series ... (previous) ... (next): Chapter Two: $\S 1$. Piecewise-Continuous Functions
- 1961: David V. Widder: Advanced Calculus (2nd ed.) ... (previous) ... (next): $1$ Partial Differentiation: $\S 2$. Functions of One Variable: $2.2$ Derivatives: Definition $2$
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): left and right derivative