Question

How do you implicitly differentiate `18=(y-x)^2-ln(xy)`?

Answer 1

`(2(y-x)+1/x)/(2(y-x)-1/y )=dy/dx`

Explanation:

`18=(y-x)^2-ln(xy)`

`0=-2(y-x)+2(y-x)dy/dx - (y/(xy)+x/(xy) dy/dx)`

`0=-2(y-x)+2(y-x)dy/dx - 1/x-1/y dy/dx`

`2(y-x)+1/x=2(y-x)dy/dx-1/y dy/dx`

`2(y-x)+1/x=(2(y-x)-1/y )dy/dx`

`(2(y-x)+1/x)/(2(y-x)-1/y )=dy/dx`