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INT

  • 2 years ago

find the partial derivatives with respect to x and y, if f(x,y) = \[\sum_{n=0}^{}\] (xy)^n

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  1. INT
    • 2 years ago
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    |xy| <1

  2. Ahaanomegas
    • 2 years ago
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    So, wrt to one variable, you treat the other as a constant. So how would you differentiate (constant*x)^n?

  3. INT
    • 2 years ago
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    (n)x^(n-1)? but what about the sum?

  4. Ahaanomegas
    • 2 years ago
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    @First question - Yep. @Second question - What's the upper limit? Also, what's the |xy| < 1 for? Sorry, I'm not quite understanding the question fully.

  5. INT
    • 2 years ago
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    the upper limit is infinity. |xy|<1 is the condition that goes along with the question

  6. Ahaanomegas
    • 2 years ago
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    Ah! Makes sense. So, basically, for x, it would be: \[ \displaystyle\sum_{n=0}^{\infty} nx^{n-1}. \]At this point, I'll just wait for another response. I really have no idea myself. Sorry. :( All the best!

  7. nitz
    • 2 years ago
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    patial derivative wrt to x \[\sum_{n=0}^{n=\infty}nx ^{n-1}y ^{n}\]

  8. nitz
    • 2 years ago
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    and wrt to y \[\sum_{n=0}^{n=\infty}x ^{n}(ny ^{n-1})\]

  9. nitz
    • 2 years ago
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    any query?

  10. INT
    • 2 years ago
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    I dont think that is quite right. I dont get how you take a partial of a sum and how you would account for |xy| < 1

  11. nitz
    • 2 years ago
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    ok first tell me the partial derivative of xy^3

  12. nitz
    • 2 years ago
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    wrt to x??????

  13. nitz
    • 2 years ago
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    just find out and tell me

  14. INT
    • 2 years ago
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    find 2 different partials, one with relation to x and one with relation to y

  15. nitz
    • 2 years ago
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    ya u find

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