Question

What is the implicit derivative of `-2=xy^2-3xy`?

Answer 1

I found: `(dy)/(dx)=(y(3-y))/(x(2y-3))`

Explanation:

The idea is that you need to derive `y` as well as it represents a function of `x`; so, for example to derive `y^2` you get: `2y(dy)/(dx)`!
Where the `(dy)/(dx)` bit takes into accont the `x` dependence of `y`:

in your case you'll get:
`0=1*y^2+2xy(dy)/(dx)-3y-3x*1(dy)/(dx)`
where I used the Product Rule;
collect: `(dy)/(dx)`:
`(dy)/(dx)[2xy-3x]=3y-y^2`
`(dy)/(dx)=(y(3-y))/(x(2y-3))`