partial differentiation

**ashes** · April 8th 2008, 11:46 PM

Hi guys,some help on this.. $v=\log_e(e^x+e^y+e^z)\mbox{verify that}\ \frac{\delta\nu}{\delta\mbox{x}}+\frac{\delta\nu}{ \delta\mbox{y}}+\frac{\delta\nu}{\delta\mbox{z}}=1$

**earboth** · April 9th 2008, 12:12 AM

Originally Posted by ashes

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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