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Math Help - Partial Differentiation

  1. #1
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    Question Partial Differentiation

    Hi guys could you please help me with this question-


    For an arbitrary function f = f(u, v) show that

    1/x(df/dx) + 1/y(df/dy) = 4(df/du)

    where u = x^2 + y^2, v = x^2 − y^2,

    x not = 0 and y not = 0
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  2. #2
    MHF Contributor arbolis's Avatar
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    Quote Originally Posted by rologolfer View Post
    Hi guys could you please help me with this question-


    For an arbitrary function f = f(u, v) show that

    1/x(df/dx) + 1/y(df/dy) = 4(df/du)

    where u = x^2 + y^2, v = x^2 − y^2,

    x not = 0 and y not = 0
    By the chain rule, \frac{\partial f}{\partial x}= \frac{\partial f}{\partial u} \cdot \frac{\partial u}{\partial x}+\frac{\partial f}{\partial v} \cdot \frac{\partial v}{\partial x}.
    Does this help?
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  3. #3
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    Thanks a lot, thats great!
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