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Math Help - partial differentiation

  1. #1
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    partial differentiation

    Hi guys,some help on this.. v=\log_e(e^x+e^y+e^z)\mbox{verify that}\ \frac{\delta\nu}{\delta\mbox{x}}+\frac{\delta\nu}{  \delta\mbox{y}}+\frac{\delta\nu}{\delta\mbox{z}}=1
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  2. #2
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    Quote Originally Posted by ashes View Post
    Hi guys,some help on this.. v=\log_e(e^x+e^y+e^z)\mbox{verify that}\ \frac{\delta\nu}{\delta\mbox{x}}+\frac{\delta\nu}{  \delta\mbox{y}}+\frac{\delta\nu}{\delta\mbox{z}}=1
    Use chain rule:

    v' = \frac1{e^x+e^y+e^z} \cdot e^x +\frac1{e^x+e^y+e^z} \cdot e^y+\frac1{e^x+e^y+e^z} \cdot e^z

    Therefore:

    v'=\frac{e^x+e^y+e^z}{e^x+e^y+e^z} = 1
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