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Please help me find the first derivative, dy/dx, of $(xy)^x=e$

Wolfram alpha gives me the solution, how they explained to get there is confusing

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Welcome to MSE! Can you show us what you have tried and why you are confused? Also, it helps to format question in laTex / MathJax for readability. Regards –  Amzoti Mar 11 '13 at 12:45
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1 Answer

Product Rule is what you need to know and to check your answer see here

$\frac{d}{dx} x\ln \left(xy\right) = \ln(xy)+1$

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If you put = 1 in wolfram apha and find the dy/dx of the problem, it's a completely different answer that uses the chain and product rule. That's where it loses me –  Sam Mar 11 '13 at 12:52
    
what? you question is a bit unclear why do you try to differentiate 1? One is a constant, thus when you differentiate a constant it equals zero. Also, are you in the Reals or Complex or some other metric space? Are you asking for which value of $x$ or $y$ will make the derivative equal to one? –  yiyi Mar 11 '13 at 12:56
    
Sorry, I'm trying to find y'. I would need to use the product and chain rule to do so. That's what confusing me –  Sam Mar 11 '13 at 13:01
    
@sam are you doing differential equations? why do you have the derivative in terms of x? –  yiyi Mar 11 '13 at 13:05
    
To make this slightly clearer. The problem I am working asks me to find the first derivative, dy/dx, of (xy)^x = e –  Sam Mar 11 '13 at 13:11
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