Question

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

Answer 1

I found: `(dy)/(dx)=[2xyln(y)]/(y-x^2)`

Explanation:

Here you need to consider `y` as a function of `x` and so differentiate it as well.
You'll get:
`0=2xln(y)+x^2*1/y(dy)/(dx)-1*(dy)/(dx)`
collect `(dy)/(dx)`:
`(dy)/(dx)=-[2xln(y)]/(x^2/y-1)=[2xyln(y)]/(y-x^2)`