# How do you find dy/dx for y + 2x - 3xy^3 = 4?

May 26, 2015

You must remember that $y$ is a function of $x$ so that to take into account this you have to include $\frac{\mathrm{dy}}{\mathrm{dx}}$ when deriving any $y$ in your function, as:
$1 \frac{\mathrm{dy}}{\mathrm{dx}} + 2 - 3 {y}^{3} - 9 x {y}^{2} \frac{\mathrm{dy}}{\mathrm{dx}} = 0$
Collecting $\frac{\mathrm{dy}}{\mathrm{dx}}$:
$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{3 {y}^{3} - 2}{1 - 9 x {y}^{2}}$