# What is the implicit derivative of 1=y^2-5xy?

Aug 1, 2016

$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{- 5 y}{5 x - 2 y}$

#### Explanation:

Differentiate term by term. As $y \left(x\right)$ is a function of $x$ we must use the chain rule.

$\frac{d}{\mathrm{dx}} \left(1\right) = \frac{d}{\mathrm{dx}} \left({y}^{2}\right) - \frac{d}{\mathrm{dx}} \left(5 x y\right)$

$0 = 2 y \frac{\mathrm{dy}}{\mathrm{dx}} - 5 y - 5 x \frac{\mathrm{dy}}{\mathrm{dx}}$

Group like terms:

$\frac{\mathrm{dy}}{\mathrm{dx}} \left(5 x - 2 y\right) = - 5 y$

$\therefore \frac{\mathrm{dy}}{\mathrm{dx}} = \frac{- 5 y}{5 x - 2 y}$