Simplification Help: Can't Simplify Further?

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Homework Help Overview

The discussion revolves around the simplification of an expression derived from implicit differentiation, specifically related to the equation x^{6}e^{-2y}=ln(xy). Participants are exploring the steps taken to arrive at a particular form and questioning the validity of that form.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the simplification of an expression and express uncertainty about whether it can be simplified further. There are inquiries about the correctness of the derived expression and requests for clarification on the steps taken to reach that point.

Discussion Status

The discussion is ongoing, with participants sharing their thoughts on the simplification process and questioning the accuracy of the results. Some guidance has been offered regarding the need to recalculate derivatives, indicating a potential direction for further exploration.

Contextual Notes

There is mention of a perceived error in the final answer, which suggests that assumptions or calculations may need to be revisited. Participants are encouraged to clarify their methods and reasoning.

7yler
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I have worked a question down to this, but I am not sure how to simplify any further.

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I think that has been simplified enough. I see no way to simplify it any further...
 
= 3 - \frac{3x+y}{x\left(2yx^5 e^{-2y} -1\right)} ??

But that's not really simplification :))
 
The original question was: suppose x^{6}e^{-2y}=ln(xy)

Find \frac{dy}{dx} by implicit differentiation.

That is the answer that I have come to, but it is said to be wrong.
 
And can you posts what you did to get to that solution?
 
Well, you should calculate once more the partial derivative wrt y.
 

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