# How do you find the derivative of x^2 y^2 + sin y = 4?

$2 x {y}^{2} + 2 y {x}^{2} \left(\frac{\mathrm{dy}}{\mathrm{dx}}\right) + \cos y \left(\frac{\mathrm{dy}}{\mathrm{dx}}\right) = 0$
$2 y {x}^{2} \left(\frac{\mathrm{dy}}{\mathrm{dx}}\right) + \cos y \left(\frac{\mathrm{dy}}{\mathrm{dx}}\right) = 0 - 2 x {y}^{2}$
$\frac{\mathrm{dy}}{\mathrm{dx}} \left(2 y {x}^{2} + \cos y\right) = - 2 x {y}^{2}$
$\frac{\mathrm{dy}}{\mathrm{dx}} = - \frac{2 x {y}^{2}}{2 y {x}^{2} + \cos y}$