Confusing problem. Please help with differentiation

Question

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

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

yiyi · Answer 1 · 2013-03-11 12:45:38Z

up vote 1 down vote

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

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

answered Mar 11 at 12:45

yiyi
1,966422

	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 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 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 at 13:01
	@sam are you doing differential equations? why do you have the derivative in terms of x? – yiyi Mar 11 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 at 13:11

1 Answer