I don't really understand how to do this but I tried to do a problem. Here's my work.

The problem is $\displaystyle 2x^3 + x^2 y - x y^3 = 2$

sorry I put up the work to another problem here's the real work:

$\displaystyle 2x^3 + (2xy + x^2 y') - (y^3 + y') = 0 $

I moved everything except y' to one side and I got this:

$\displaystyle y' = \frac {-2x^3 - 2xy + y^3}{x^2 - 1}$

I have a feeling that I messed up somewhere but I don't know where since I do not fully understand Implicity Differentiation.