Let $g ( x , y ) = \left( x ^ { 2 } + y ^ { 2 } \right) f ( x , y )$

True/False

Let $g ( x , y ) = \left( x ^ { 2 } + y ^ { 2 } \right) f ( x , y )$ , where $f ( x , y ) = \left\{ \begin{array} { l l } - | y | & | y | \leq | x | \\- | x | & | x | \leq | y |\end{array} \right.$ g is differentiable at (0,0).