Quotient rule

This is similar to the product rule except that it applies to quotients. We can deduce it by differentiating using the product and chain rules. First, by the chain rule . By the product rule,

$$\begin{eqnarray*} \frac{\mathrm{d}y}{\mathrm{d}x} & = & v^{-1} \frac{\mathrm{d}u... ...thrm{d}u}{\mathrm{d}x} - u \frac{\mathrm{d}v}{\mathrm{d}x}}{v^2} \end{eqnarray*}$$

This is the quotient rule used to differentiate a quotient of functions such as . Here, we put , so that . Hence, .