$\therefore $ ${\left( {\frac{{\partial u}}{{\partial x}}} \right)^2} = \frac{9}{4}({x^2} + {y^2} + {z^2})4{x^2} = 9{x^2}({x^2} + {y^2} + {z^2})$
$\therefore $ ${\left( {\frac{{\partial u}}{{\partial x}}} \right)^2} + {\left( {\frac{{\partial u}}{{\partial y}}} \right)^2} + {\left( {\frac{{\partial u}}{{\partial z}}} \right)^2}$
$= 9\,({x^2} + {y^2} + {z^2})\,({x^2} + {y^2} + {z^2})$
$= 9\,{({x^2} + {y^2} + {z^2})^2}$ = $9.{u^{4/3}}$.
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