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Math Help - Differentiation problem

  1. #1
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    Differentiation problem



    2006
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  2. #2
    Junior Member
    Joined
    Feb 2009
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    30
    u = \phi(x - y, y - z, z - x) = \phi(a_1, a_2, a_3)

    a_1 = x - y
    a_2 = y - z
    a_3 = z - x

    \frac{du}{dx} = \sum_{i = 1}^{3}\frac{d\phi}{da_i}\frac{da_i}{dx} = \frac{d\phi}{da_1} - \frac{d\phi}{da_3}
    \frac{du}{dy} = -\frac{d\phi}{da_1} + \frac{d\phi}{da_2}
    \frac{du}{dz} = -\frac{d\phi}{da_2} + \frac{d\phi}{da_3}

    \Rightarrow \frac{du}{dx} + \frac{du}{dy} + \frac{du}{dz} = \frac{d\phi}{da_1} - \frac{d\phi}{da_3} - \frac{d\phi}{da_1} + \frac{d\phi}{da_2} - \frac{d\phi}{da_2} + \frac{d\phi}{da_3} = 0
    yey!! ^^
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