Right derivative ($f_{+}^{\prime }(a)={\lim }_{h\downarrow 0}\frac{f(a+h)-f(a)}{h}$)

The right derivative is the displayed one-sided limit, when it exists as a finite number. It describes differentiation at the left endpoint of a closed interval without requiring the function to be defined to the left. An ordinary derivative at an interior point requires matching left and right derivatives. For example, the absolute value function has right derivative one at zero and left derivative minus one, so it has no ordinary derivative there.