Question

partial derivative f(w,z) = w/(w^2+z^2)

Answer 1

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

Answer 2

how would you use this as a product rule?

Answer 3

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

Answer 4

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

Answer 5

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

Answer 6

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

Answer 7

yeap so then \[1(w^2+z^2)-w(2w)/ (w^2+z^2)^2\]

Answer 8

?

Answer 9

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

Answer 10

yeah i know

Answer 11

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

Answer 12

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

Answer 13

Yah looks good for fz c:

Answer 14

thanks