Question

How do you differentiate `y=x^2y-y^2x`?

Answer 1

I found: `(dy)/(dx)=(2xy-y^2)/(-x^2+2yx+1)`

Explanation:

We use Implicit Differentiation where we remember that `y` is a function of `x` and must be derived accordingly;
for example if you have `y^2` you derive it getting: `2y(dy)/(dx)` to take into account this depndence.

In your case we get:

`1(dy)/(dx)=2xy+x^2(dy)/(dx)-2yx(dy)/(dx)-y^2`
collect `(dy)/(dx)` and rearrange:
`(dy)/(dx)=(2xy-y^2)/(-x^2+2yx+1)`