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math_proof Group Title

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

  • one year ago
  • one year ago

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  1. cruffo Group Title
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    Are you thinking of using quotient rule or product rule for this one?

    • one year ago
  2. math_proof Group Title
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    how would you use this as a product rule?

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

    • one year ago
  4. cruffo Group Title
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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.

    • one year ago
  5. math_proof Group Title
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    i think the whole point of this problem is to remind myself of quotient rule lol

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

    • one year ago
  7. math_proof Group Title
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    yeap so then \[1(w^2+z^2)-w(2w)/ (w^2+z^2)^2\]

    • one year ago
  8. math_proof Group Title
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    ?

    • one year ago
  9. cruffo Group Title
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    Yes. Though it can be simplified by gathering like terms in the numerator.

    • one year ago
  10. math_proof Group Title
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    yeah i know

    • one year ago
  11. cruffo Group Title
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    I figured you did :) But better to mention it than not.

    • one year ago
  12. math_proof Group Title
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    for fz is -2zw/(w^2+z^2)^2?

    • one year ago
  13. zepdrix Group Title
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    Yah looks good for fz c:

    • one year ago
  14. math_proof Group Title
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    thanks

    • one year ago
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