QuotientRule 2002-05-17 22:38:03 2002-05-18 20:17:09 Theorem calculus derivative fractions derivatives % this is the default PlanetMath preamble. as your knowledge % of TeX increases, you will probably want to edit this, but % it should be fine as is for beginners. % almost certainly you want these \usepackage{amssymb} \usepackage{amsmath} \usepackage{amsfonts} % used for TeXing text within eps files %\usepackage{psfrag} % need this for including graphics (\includegraphics) %\usepackage{graphicx} % for neatly defining theorems and propositions %\usepackage{amsthm} % making logically defined graphics %\usepackage{xypic} % there are many more packages, add them here as you need them % define commands here The \emph{quotient rule} says that the derivative of the quotient \(f/g\) of two differentiable functions \(f\) and \(g\) exists at all values of \(x\) as long as \(g(x) \not= 0\) and is given by the formula \begin{equation*} \frac{d}{dx}\ \left[\frac{f(x)}{g(x)}\ \right] = \frac{g(x)f'(x) - f(x)g'(x)}{\lbrack g(x) \rbrack ^2} \end{equation*} The Quotient Rule and the other differentiation formulas allow us to compute the derivative of any rational function.