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Math Help - Is this wrong? (differential operator)

  1. #1
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    Is this wrong? (differential operator)

    I believe this soln has an error.



    Am I right?
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by scorpion007 View Post
    I believe this soln has an error.



    Am I right?
    What is F? What are x and y?
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  3. #3
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    Sorry, I didn't think it mattered, given the context. But here they are:



    The reason I say it's wrong is because when you distribute the x through the first term, you end up with x^2 and similarly for the second term with y.

    (Also, we assume the mixed derivatives are equal)
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  4. #4
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by scorpion007 View Post
    Sorry, I didn't think it mattered, given the context. But here they are:



    The reason I say it's wrong is because when you distribute the x through the first term, you end up with x^2 and similarly for the second term with y.

    (Also, we assume the mixed derivatives are equal)
    We needed to know that x=x(s),y=y(s)

    And so you're just applying the chain rule? That is what that jpeg is of, right? Double application of the chain rule?
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  5. #5
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    Isn't x = x(s, t) and y = y(s, t)?

    Yes, this is the chain rule for partial derivs.
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