How do you differentiate x^4+2y^2=8?

I found: $\frac{\mathrm{dy}}{\mathrm{dx}} = - {x}^{3} / y$
You use implicit differentiation remembering that $y$ is a function of $x$.
$4 {x}^{3} + 4 y \textcolor{red}{\frac{\mathrm{dy}}{\mathrm{dx}}} = 0$
$\frac{\mathrm{dy}}{\mathrm{dx}} = - \cancel{4} {x}^{3} / \left(\cancel{4} y\right) = - {x}^{3} / y$