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Math Help - help needed for partial D qn

  1. #1
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    help needed for partial D qn

    Hi All,
    I got a problem tat i cant solve. pls help!

    w is a function
    w= -x to the power of 1/2 x F(z)

    and z= y/2 x 1/( x to the pwer of 1/2)


    the qns are as follow:

    if u = -(dz/dy)
    derive an expression for u in terms of F' where F' is dF/dz

    Thanks for your help!

    Jae
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  2. #2
    MHF Contributor

    Joined
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    Please don't use "x" both for a variable and as a multiplication sign! Use "*" or, better, use LaTex.

    I think you mean that
    w= -x^{1/2}F(z)
    which also says that x^{1/2}= -\frac{w}{F(z)}

    z= \frac{y}{2}\frac{1}{x^{1/2}}

    Those two together tell us that
    z= -\frac{y}{2}\frac{F(z)}{w}

    It isn't clear whether w is independent of y or not. Assuming it is, we can differentiate both sides with respect to y to get
    \frac{dz}{dy}= -\frac{1}{2}\frac{F(z)}{w}- \frac{y}{2}\frac{F'(z)}{w}\frac{dz}{dy}

    Solve that algebraically for u.
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