anonymous
  • anonymous
How do I partially differentiate f = 2x/(x^2 +y^2) wrt x and y? Is it by the quotient rule? Any help is very much appreciated.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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experimentX
  • experimentX
by treating one as constant
anonymous
  • anonymous
quotient rule needed for \(f_x\) but not for \(f_y\) since in that case you view \(2x\) as a constant
anonymous
  • anonymous
Thank you

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anonymous
  • anonymous
who nellie, you are differentiating not integrating.
anonymous
  • anonymous
\[f_x=\frac{(x^2+y^2)2-x^2(2x)}{(x^2+y^2)^2}\] then some algebra to clean it up
anonymous
  • anonymous
thnxxxxxx
anonymous
  • anonymous
\(f_y\) is easier because you treat the numerator as a constant you get \[f_y=-\frac{2y}{(x^2+y^2)^2}\]
anonymous
  • anonymous
I ended up getting 2/(x^2 + y^2) - 4x^2/(x^2 +y^2)^2 for the partial derivative wrt x and -4yx/(x^2 +y^2) for y. Any idea where I might be going wrong? Thanks again
anonymous
  • anonymous
maybe i made a mistake. lets do it for \(f_y\)
anonymous
  • anonymous
oh right, doh you are rigth about \(f_y\)
anonymous
  • anonymous
well, except the denominator should be squared
anonymous
  • anonymous
Why is that?
anonymous
  • anonymous
quotient rule
anonymous
  • anonymous
or in this case just \[\frac{d}{dy}\frac{1}{f(y)}=-\frac{f'(y)}{f^2(y)}\]
anonymous
  • anonymous
first one it looks like you are using the product rule, so i might be the same as my answer
anonymous
  • anonymous
oh yes, you are right. i missed a 2 from the 2x up top you are correct
anonymous
  • anonymous
Ah, fantastic. Thanks a million.

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