Implicit differentiation

In summary, the conversation is about a question on how to isolate dy/dx on one side after implicitly differentiating the equation x/y + y/x = 2y. The person has tried differentiating the LHS by its terms and getting the common denominator, but is still unable to isolate dy/dx. They are wondering if there is a way to do so.
  • #1
physicsernaw
41
0

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).
 
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  • #2
physicsernaw said:

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 .
 

What is implicit differentiation?

Implicit differentiation is a mathematical technique used to find the derivative of a function when the equation is given implicitly, meaning that the dependent and independent variables are not explicitly stated.

Why is implicit differentiation used?

Implicit differentiation is used when the dependent and independent variables in a function are not explicitly stated. In these cases, it is not possible to find the derivative using the standard methods of differentiation, so implicit differentiation is used instead.

How is implicit differentiation done?

To perform implicit differentiation, the equation is first rewritten in the form y = f(x). Then, the derivative of both sides of the equation is taken with respect to x, treating y as a function of x. The result is an equation that can be solved for dy/dx, the derivative of y with respect to x.

What is the chain rule in implicit differentiation?

The chain rule is a fundamental rule in calculus that is used when taking the derivative of a composite function. In implicit differentiation, the chain rule is used to find the derivative of the dependent variable with respect to the independent variable.

What are some applications of implicit differentiation?

Implicit differentiation has many applications in mathematics and science, including optimization problems, curve sketching, and finding rates of change in real-world situations. It is also used in higher-level mathematics and physics to solve more complex equations.

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