anonymous
  • anonymous
find the partial derivatives with respect to x and y, if f(x,y) = \[\sum_{n=0}^{}\] (xy)^n
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
|xy| <1
anonymous
  • anonymous
So, wrt to one variable, you treat the other as a constant. So how would you differentiate (constant*x)^n?
anonymous
  • anonymous
(n)x^(n-1)? but what about the sum?

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anonymous
  • anonymous
@First question - Yep. @Second question - What's the upper limit? Also, what's the |xy| < 1 for? Sorry, I'm not quite understanding the question fully.
anonymous
  • anonymous
the upper limit is infinity. |xy|<1 is the condition that goes along with the question
anonymous
  • anonymous
Ah! Makes sense. So, basically, for x, it would be: \[ \displaystyle\sum_{n=0}^{\infty} nx^{n-1}. \]At this point, I'll just wait for another response. I really have no idea myself. Sorry. :( All the best!
anonymous
  • anonymous
patial derivative wrt to x \[\sum_{n=0}^{n=\infty}nx ^{n-1}y ^{n}\]
anonymous
  • anonymous
and wrt to y \[\sum_{n=0}^{n=\infty}x ^{n}(ny ^{n-1})\]
anonymous
  • anonymous
any query?
anonymous
  • anonymous
I dont think that is quite right. I dont get how you take a partial of a sum and how you would account for |xy| < 1
anonymous
  • anonymous
ok first tell me the partial derivative of xy^3
anonymous
  • anonymous
wrt to x??????
anonymous
  • anonymous
just find out and tell me
anonymous
  • anonymous
find 2 different partials, one with relation to x and one with relation to y
anonymous
  • anonymous
ya u find

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