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

Definition of a Derivative
If $y = f \left({x}\right)$, the derivative of $y$ or $f \left({x}\right)$ with respect to $x$ is defined as:
 * $13.1$: $\displaystyle \frac {\mathrm d y} {\mathrm d x} = \lim_{h \to 0} \frac {f \left({x + h}\right) - f \left({x}\right)} h = \lim_{\Delta x \to 0} \frac {f \left({x + \Delta x}\right) - f \left({x}\right)} {\Delta x}$

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