Question

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.

Answer 1

by treating one as constant

Answer 2

quotient rule needed for \(f_x\) but not for \(f_y\) since in that case you view \(2x\) as a constant

Answer 3

Thank you

Answer 4

who nellie, you are differentiating not integrating.

Answer 5

\[f_x=\frac{(x^2+y^2)2-x^2(2x)}{(x^2+y^2)^2}\] then some algebra to clean it up

Answer 6

thnxxxxxx

Answer 7

\(f_y\) is easier because you treat the numerator as a constant
you get
\[f_y=-\frac{2y}{(x^2+y^2)^2}\]

Answer 8

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

Answer 9

maybe i made a mistake. lets do it for \(f_y\)

Answer 10

oh right, doh
you are rigth about \(f_y\)

Answer 11

well, except the denominator should be squared

Answer 12

Why is that?

Answer 13

quotient rule

Answer 14

or in this case just
\[\frac{d}{dy}\frac{1}{f(y)}=-\frac{f'(y)}{f^2(y)}\]

Answer 15

first one it looks like you are using the product rule, so i might be the same as my answer

Answer 16

oh yes, you are right. i missed a 2 from the 2x up top
you are correct

Answer 17

Ah, fantastic. Thanks a million.