Solving a Calculus Problem with Implicit Differentiation

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Homework Help Overview

The discussion revolves around a calculus problem involving implicit differentiation. The original poster is attempting to find dy/dx and is seeking confirmation on their approach and algebraic manipulations.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster shares an image of their work and expresses uncertainty about their algebra skills. They inquire whether they are on the right track with implicit differentiation. Participants discuss the correct application of differentiation rules, particularly the chain rule, and clarify where the original poster may have misunderstood the differentiation of terms.

Discussion Status

Participants are actively engaging with the original poster's work, providing feedback on specific lines of differentiation. Some guidance has been offered regarding the application of the chain rule, and there appears to be a collaborative effort to clarify misunderstandings without reaching a definitive conclusion.

Contextual Notes

The original poster mentions having rusty algebra skills, which may influence their confidence in solving the problem. There is also a reference to an attached image that is central to the discussion, but its content is not described in detail.

Jason03
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Heres another problem I was working on...

http://img141.imageshack.us/img141/2318/calc2qg4.jpg

Im trying to find dy/dx using implicit differentiation...my algebra is a bit rusty...but I am trying to make sure I am on the right track...
 
Last edited by a moderator:
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Implicit diff of x^2 is not 2xy', it's just 2x. Everything else is fine.
 
where did I do that in the problem?
 
Not quite;

When you are differentiating x2 with respect to x, for example, you simply get 2x. You do not multiply 2x by dy/dx.

However, when you (implicitly) differentiate y2 with respect to x (where y is a function of x) you get

[tex] 2y \frac{dy}{dx}[/tex]

Here you do multiply by dy/dx; the reason comes from the chain rule.
 
Jason03 said:
where did I do that in the problem?

Third line, first expression on the left hand side (referring to your attached image)
 
like this?

http://img375.imageshack.us/img375/5230/calc3eh3.jpg
 
Last edited by a moderator:
does the work above look ok?
 
Jason03 said:
does the work above look ok?

Looks fine to me
 

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