Question

How do you use implicit differentiation to find dy/dx for `x^2y+xy^2=10`?

Answer 1

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

Explanation:

You must remember that `y` is a function of `x` (as `y=f(x)`) when differentiating:
`2xy+x^2(dy)/(dx)+y^2+2xy(dy)/(dx)=0` (where I used the Product Rule);
So collecting `(dy)/(dx)` you get:
`(dy)/(dx)=-(2xy+y^2)/(2xy+x^2)`