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Math Help - Showing polar coordinate partial derivative stuff

  1. #1
    s3a
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    Showing polar coordinate partial derivative stuff

    Could someone please help get me started on this problem?

    For part (a), I always took for granted as if it were by definition but maybe it's defined in the regular xy plane and then deduced in the polar form? If I'm right, how do I start specifically? If I'm wrong then what do I do?

    As for part (b), that's just applying part (a) mechanically, right?

    Any help in solving this problem would be greatly appreciated!
    Thanks in advance!
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  2. #2
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    Re: Showing polar coordinate partial derivative stuff

    Are you allowed to use the definition of the gradient in curvilinear coordinates?
    Gradient -- from Wolfram MathWorld

    b) Use the answer from a) and then simply find the partial derivatives \frac{\partial u}{\partial r} and \frac{\partial u}{\partial \theta}.
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