quotient rule

The 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 $g(x)\ne 0$ and is given by the formula

$$\frac{d}{dx}\left[\frac{f(x)}{g(x)}\right]=\frac{g(x)f^{\prime }(x)-f(x)g^{\prime }(x)}{{[g(x)]}^2}$$

The Quotient Rule and the other differentiation formulas allow us to compute the derivative of any rational function.