$\frac{f\left(x_{0}+h\right)-f\left(x_{0}\right)}{h}, \quad h \neq 0$ is called the **difference quotient** of $f$ at ${x}_{0}$ with increment $h$. If the difference quotient has a [[Limit (ε, δ)|limit]] as $h$ approaches zero, that limit is given a special name and notation: the [[Derivative at a point|derivative at]] $x_0 $, $f^\prime(x_0)$