# How do you differentiate xy=pi/6?

Jan 31, 2017

$\frac{\mathrm{dy}}{\mathrm{dx}} = - \frac{y}{x}$

#### Explanation:

differentiate $\textcolor{b l u e}{\text{implicitly with respect to x}}$

Using the $\textcolor{b l u e}{\text{product rule}}$ to differentiate the term xy

$\Rightarrow \left(x . \frac{\mathrm{dy}}{\mathrm{dx}}\right) + \left(y . \frac{d}{\mathrm{dx}} \left(x\right)\right) = 0$

$\Rightarrow x \frac{\mathrm{dy}}{\mathrm{dx}} + y = 0 \Rightarrow x \frac{\mathrm{dy}}{\mathrm{dx}} = - y$

$\Rightarrow \frac{\mathrm{dy}}{\mathrm{dx}} = - \frac{y}{x}$