Simplification Help: Can't Simplify Further?

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The discussion centers on the implicit differentiation of the equation x6e-2y = ln(xy) to find dy/dx. The user believes they have simplified the expression to 3 - (3x + y) / (x(2yx5e-2y - 1)), but doubts its correctness. Another participant suggests recalculating the partial derivative with respect to y to verify the solution. The key takeaway is the importance of accurately applying implicit differentiation techniques in calculus.

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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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