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math_proof

  • 3 years ago

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

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  1. cruffo
    • 3 years ago
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    Are you thinking of using quotient rule or product rule for this one?

  2. math_proof
    • 3 years ago
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    how would you use this as a product rule?

  3. cruffo
    • 3 years ago
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    \[\large f(w,z) =\frac{w}{w^2+z^2} = w\left(w^2+z^2\right)^{-1}\]

  4. cruffo
    • 3 years ago
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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.

  5. math_proof
    • 3 years ago
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    i think the whole point of this problem is to remind myself of quotient rule lol

  6. cruffo
    • 3 years ago
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    :) If \(f = \dfrac{u}{v}\), then \(f' = \dfrac{u'v - uv'}{v^2}\)

  7. math_proof
    • 3 years ago
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    yeap so then \[1(w^2+z^2)-w(2w)/ (w^2+z^2)^2\]

  8. math_proof
    • 3 years ago
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    ?

  9. cruffo
    • 3 years ago
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    Yes. Though it can be simplified by gathering like terms in the numerator.

  10. math_proof
    • 3 years ago
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    yeah i know

  11. cruffo
    • 3 years ago
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    I figured you did :) But better to mention it than not.

  12. math_proof
    • 3 years ago
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    for fz is -2zw/(w^2+z^2)^2?

  13. zepdrix
    • 3 years ago
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    Yah looks good for fz c:

  14. math_proof
    • 3 years ago
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    thanks

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