Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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

share|cite|improve this question
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

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

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

share|cite|improve this answer
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

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.