Implicit differentiation

  • #1

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).
 

Answers and Replies

  • #2
SammyS
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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 .
 

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