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**bluntpencil** Okay,

I understand that if a differentiable function $\displaystyle z=f(g(x,y))$ and x, y are the independent variables, then

$\displaystyle \frac{\partial{g}}{\partial{x}} = \lim_{\delta{x}\to{0}}\left(\frac{\delta{g}}{\delt a{x}}\right)$ and $\displaystyle \frac{\partial{f}}{\partial{g}} = \lim_{\delta{g}\to{0}}\left(\frac{\delta{f}}{\delt a{g}}\right)$, so $\displaystyle \frac{\partial{f}}{\partial{x}} = \frac{\partial{f}}{\partial{g}}.\frac{\partial{g}} {\partial{x}}$, keeping y constant

and

$\displaystyle \frac{\partial{g}}{\partial{y}} = \lim_{\delta{y}\to{0}}\left(\frac{\delta{g}}{\delt a{y}}\right)$ and $\displaystyle \frac{\partial{f}}{\partial{g}} = \lim_{\delta{g}\to{0}}\left(\frac{\delta{f}}{\delt a{g}}\right)$, so $\displaystyle \frac{\partial{f}}{\partial{y}} = \frac{\partial{f}}{\partial{g}}.\frac{\partial{g}} {\partial{y}}$, keeping x constant

now, if I let $\displaystyle u=g(x, y)$ can someone show/explain using the above method what $\displaystyle \frac{\partial{z}}{\partial{u}}$ would be?.

Thanks.