kingdan1550
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.
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experimentX
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by treating one as constant
anonymous
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quotient rule needed for \(f_x\) but not for \(f_y\) since in that case you view \(2x\) as a constant
kingdan1550
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Thank you
anonymous
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who nellie, you are differentiating not integrating.
anonymous
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\[f_x=\frac{(x^2+y^2)2-x^2(2x)}{(x^2+y^2)^2}\] then some algebra to clean it up
niki
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thnxxxxxx
anonymous
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\(f_y\) is easier because you treat the numerator as a constant
you get
\[f_y=-\frac{2y}{(x^2+y^2)^2}\]
kingdan1550
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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
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maybe i made a mistake. lets do it for \(f_y\)
anonymous
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oh right, doh
you are rigth about \(f_y\)
anonymous
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well, except the denominator should be squared
kingdan1550
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Why is that?
anonymous
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quotient rule
anonymous
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or in this case just
\[\frac{d}{dy}\frac{1}{f(y)}=-\frac{f'(y)}{f^2(y)}\]
anonymous
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first one it looks like you are using the product rule, so i might be the same as my answer
anonymous
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oh yes, you are right. i missed a 2 from the 2x up top
you are correct
kingdan1550
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Ah, fantastic. Thanks a million.