Question

How do you implicitly differentiate `sqrt(xy) = x - 2y`?

Answer 1

`y'=(2sqrt(xy)-y)/(x+4sqrt(xy))`

Explanation:

`1/(2sqrt(xy)) [xy'+y]=1-2y'`

`xy'+y =(1-2y')(2sqrt(xy))`

`xy'+y=2sqrt(xy)-4y'sqrt(xy)`

`xy'+4y'sqrt(xy)=2sqrt(xy)-y`

`y'(x+4sqrt(xy))=2sqrt(xy)-y`

`y'=(2sqrt(xy)-y)/(x+4sqrt(xy))`