If \(f(x,y)\) is a function of the two independent variables \(x\) and \(y\), define the partial derivatives \(\frac{\partial f}{\partial x}\) and \(\frac{\partial f}{\partial y}\). \newline The identical relation \(g(u^2-x^2, u^2-y^2, u^2-z^2)=0\) defines \(u\) as a function of \(x, y\) and \(z\). Shew that \[ \frac{1}{x}\frac{\partial u}{\partial x} + \frac{1}{y}\frac{\partial u}{\partial y} + \frac{1}{z}\frac{\partial u}{\partial z} = \frac{1}{u}. \]