How Do You Isolate dy/dx in Implicit Differentiation?

[physicsernaw]

Homework Statement

Calculate the derivative with respect to x:
x/y + y/x = 2y

Homework Equations

n/a

The Attempt at a Solution

I end up getting the right answer, but what I want to know is how to isolate dy/dx to one side after implicitly differentiating. I have tried differentiating the LHS sum by its terms, and also tried getting the common denominator first of the LHS and differentiating that, but I can't isolate dy/dx.

(I understand that I could isolate y instead and take the derivative, but I wanted to know if there was a way to isolate dy/dx to one side after implicitly differentiating).

 

[SammyS]

Homework Statement

Calculate the derivative with respect to x:
x/y + y/x = 2y

Homework Equations

The Attempt at a Solution

I end up getting the right answer, but what I want to know is how to isolate dy/dx to one side after implicitly differentiating. I have tried differentiating the LHS sum by its terms, and also tried getting the common denominator first of the LHS and differentiating that, but I can't isolate dy/dx.

(I understand that I could isolate y instead and take the derivative, but I wanted to know if there was a way to isolate dy/dx to one side after implicitly differentiating).

What is your result upon implicitly differentiating?

It shouldn't be all that difficult to isolate dy/dx .