# How do you differentiate x^2y^2+xy=2?

Remember that $y$ is funcyion of $x$:
$2 x {y}^{2} + {x}^{2} \cdot 2 y \frac{\mathrm{dy}}{\mathrm{dx}} + y + x \frac{\mathrm{dy}}{\mathrm{dx}} = 0$
$\frac{\mathrm{dy}}{\mathrm{dx}} \left[2 {x}^{2} y + x\right] = - y - 2 x {y}^{2}$
$\frac{\mathrm{dy}}{\mathrm{dx}} = - \frac{y \cancel{\left(1 + 2 x y\right)}}{x \cancel{\left(2 x y + 1\right)}} = - \frac{y}{x}$