Question

How do you implicitly differentiate `-y^2=e^(xy)-y/x`?

Answer 1

`y'=(y(e^(xy)x^2+1))/(-2x^2y-x^3e^(xy)+x)`

Explanation:

we get

`-2yy'=e^(xy)(y+xy')-(y'x-y)/x^2`
Multiplying by `x^2`

`-2yy'x^2=e^(xy)x^2y+x^3y'e^(xy)-y'x+y`
so we get

`y'=(y(e^(xy)x^2+1))/(-2x^2y-x^3e^(xy)+x)`