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.

Also see

• Definition:Derivative
• Definition:Real Left-Hand Derivative

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