## 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

1. experimentX Group Title

by treating one as constant

2. satellite73 Group Title

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

3. kingdan1550 Group Title

Thank you

4. satellite73 Group Title

who nellie, you are differentiating not integrating.

5. satellite73 Group Title

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

6. niki Group Title

thnxxxxxx

7. satellite73 Group Title

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

8. kingdan1550 Group Title

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 Group Title

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

10. satellite73 Group Title

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

11. satellite73 Group Title

well, except the denominator should be squared

12. kingdan1550 Group Title

Why is that?

13. satellite73 Group Title

quotient rule

14. satellite73 Group Title

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

15. satellite73 Group Title

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

16. satellite73 Group Title

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

17. kingdan1550 Group Title

Ah, fantastic. Thanks a million.