Clearly, this function has a minimum at (0,0) yet, it is not differentiable at (0,0). How then should I show that it has a minimum at (0,0)?

$\displaystyle z= \left( {x}^{2}+{y}^{2} \right) ^{ 0.5}$

First partial:

$\displaystyle \left( {x}^{2}+{y}^{2} \right) ^{- 0.5}x$