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kingdan1550
Group Title
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.
 2 years ago
 2 years ago
kingdan1550 Group Title
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.
 2 years ago
 2 years ago

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experimentX Group TitleBest ResponseYou've already chosen the best response.0
by treating one as constant
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
quotient rule needed for \(f_x\) but not for \(f_y\) since in that case you view \(2x\) as a constant
 2 years ago

kingdan1550 Group TitleBest ResponseYou've already chosen the best response.0
Thank you
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
who nellie, you are differentiating not integrating.
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
\[f_x=\frac{(x^2+y^2)2x^2(2x)}{(x^2+y^2)^2}\] then some algebra to clean it up
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
\(f_y\) is easier because you treat the numerator as a constant you get \[f_y=\frac{2y}{(x^2+y^2)^2}\]
 2 years ago

kingdan1550 Group TitleBest ResponseYou've already chosen the best response.0
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
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
maybe i made a mistake. lets do it for \(f_y\)
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
oh right, doh you are rigth about \(f_y\)
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
well, except the denominator should be squared
 2 years ago

kingdan1550 Group TitleBest ResponseYou've already chosen the best response.0
Why is that?
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
quotient rule
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
or in this case just \[\frac{d}{dy}\frac{1}{f(y)}=\frac{f'(y)}{f^2(y)}\]
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
first one it looks like you are using the product rule, so i might be the same as my answer
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
oh yes, you are right. i missed a 2 from the 2x up top you are correct
 2 years ago

kingdan1550 Group TitleBest ResponseYou've already chosen the best response.0
Ah, fantastic. Thanks a million.
 2 years ago
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