# What is the implicit derivative of 4= (x+y)^2 -3xy?

Jan 5, 2016

I found: $\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{- 2 x + y}{2 y - x}$

#### Explanation:

You need to derive $y$ as well as it represents a function of $x$.
So, for example, if you have ${y}^{2}$ the derivative will be $2 y \frac{\mathrm{dy}}{\mathrm{dx}}$.
$0 = 2 \left(x + y\right) \cdot \left(1 + 1 \frac{\mathrm{dy}}{\mathrm{dx}}\right) - 3 y - 3 x \frac{\mathrm{dy}}{\mathrm{dx}}$
$0 = 2 x + 2 x \frac{\mathrm{dy}}{\mathrm{dx}} + 2 y + 2 y \frac{\mathrm{dy}}{\mathrm{dx}} - 3 y - 3 x \frac{\mathrm{dy}}{\mathrm{dx}}$
We collect $\frac{\mathrm{dy}}{\mathrm{dx}}$:
$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{- 2 x + y}{2 y - x}$