## math_proof 3 years ago partial derivative f(w,z) = w/(w^2+z^2)

1. cruffo

Are you thinking of using quotient rule or product rule for this one?

2. math_proof

how would you use this as a product rule?

3. cruffo

$\large f(w,z) =\frac{w}{w^2+z^2} = w\left(w^2+z^2\right)^{-1}$

4. cruffo

Though I don't think it would be much better that way. Just thought I'de get your take on it.

5. math_proof

i think the whole point of this problem is to remind myself of quotient rule lol

6. cruffo

:) If $$f = \dfrac{u}{v}$$, then $$f' = \dfrac{u'v - uv'}{v^2}$$

7. math_proof

yeap so then $1(w^2+z^2)-w(2w)/ (w^2+z^2)^2$

8. math_proof

?

9. cruffo

Yes. Though it can be simplified by gathering like terms in the numerator.

10. math_proof

yeah i know

11. cruffo

I figured you did :) But better to mention it than not.

12. math_proof

for fz is -2zw/(w^2+z^2)^2?

13. zepdrix

Yah looks good for fz c:

14. math_proof

thanks