## kingdan1550 3 years ago 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.

1. experimentX

by treating one as constant

2. satellite73

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

3. kingdan1550

Thank you

4. satellite73

who nellie, you are differentiating not integrating.

5. satellite73

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

6. niki

thnxxxxxx

7. satellite73

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

8. kingdan1550

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

9. satellite73

maybe i made a mistake. lets do it for $$f_y$$

10. satellite73

oh right, doh you are rigth about $$f_y$$

11. satellite73

well, except the denominator should be squared

12. kingdan1550

Why is that?

13. satellite73

quotient rule

14. satellite73

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

15. satellite73

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

16. satellite73

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

17. kingdan1550

Ah, fantastic. Thanks a million.