Is My Implicit Differentiation Method Correct?

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Homework Help Overview

The discussion centers around the application of implicit differentiation, specifically regarding the derivative of the expression involving the square root of the product of variables x and y. Participants are examining the correctness of the original poster's method and the simplification of their results.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the original poster's method for differentiating the expression and suggest alternative representations to clarify the differentiation process. There are inquiries about the correctness of the derived expressions and the simplification of the final answer.

Discussion Status

Some participants have provided feedback on the original poster's approach, indicating that they are on the right track after making adjustments. However, there remains a focus on the complexity of the final answer and whether it can be simplified further.

Contextual Notes

The original poster has shared images of their work, which may limit the ability to fully assess the written expressions and reasoning. There is an indication of a preference for visual representation over typed solutions.

t_n_p
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Homework Statement



http://img224.imageshack.us/img224/2459/untitledow9.jpg

Homework Equations





The Attempt at a Solution



See above picture.

I'm just curious to see if my method is correct and how exactly would I go about simplifying the answer if indeed it is correct. Thanks to anybody who can help!
 
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Your expression for the derivative of sqrt(xy) using the chain rule is in error. Y is under the square root in the expression, so the first half should be sqrt(y/x)/2. From this you should be able to get the second half.
 
Rather than writing [itex]\sqrt{xy}[/itex] as (xy)1/2, write it as x1/2y1/2. I think you will find that less confusing.
 
http://img149.imageshack.us/img149/9232/workingdh2.jpg

Thanks for pointing that out, I made the relevant changes, I hope it's a bit better now. The final answer seems very, very long winded though. Am I on the right track? Hope nobody minds me posting the pictures instead, it's easier for me than doing it on the computer!
 
Last edited by a moderator:
Yes, you're on the right track now!
 
thanks for speed reply
My final answer is...

http://img413.imageshack.us/img413/246/finalanswml7.jpg

amiright? :-p
 
Last edited by a moderator:

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