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



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

math_proof
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how would you use this as a product rule?

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

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

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

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

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

math_proof
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?

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

math_proof
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yeah i know

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

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

zepdrix
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Yah looks good for fz c:

math_proof
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thanks