Book:Murray R. Spiegel/Mathematical Handbook of Formulas and Tables/Chapter 13/Definition of a Derivative

Definition of a Derivative
If $y = \map f x$, the derivative of $y$ or $\map f x$ $x$ is defined as:
 * $13.1$: $\ds \frac {\d y} {\d x} = \lim_{h \mathop \to 0} \frac {\map f {x + h} - \map f x} h = \lim_{\Delta x \mathop \to 0} \frac {\map f {x + \Delta x} - \map f x} {\Delta x}$

where $h = \Delta x$. The derivative is also denoted by $y'$, $d f / d x$ or $\map {f'} x$. The process of taking a derivative is called differentiation.