If \[u={{({{x}^{2}}+{{y}^{2}}+{{z}^{2}})}^{3/2}}\], then \[{{\left( \frac{\partial u}{\partial x} \right)}^{2}}+{{\left( \frac{\partial u}{\partial y} \right)}^{2}}+{{\left( \frac{\partial u}{\partial z} \right)}^{2}}=\] [EAMCET 1996]

If \[u={{({{x}^{2}}+{{y}^{2}}+{{z}^{2}})}^{3/2}}\], then \[{{\left( \f

1.	If \[u={{({{x}^{2}}+{{y}^{2}}+{{z}^{2}})}^{3/2}}\], then \[{{\left( \frac{\partial u}{\partial x} \right)}^{2}}+{{\left( \frac{\partial u}{\partial y} \right)}^{2}}+{{\left( \frac{\partial u}{\partial z} \right)}^{2}}=\] [EAMCET 1996]
A.	9u
B.	\[9{{u}^{4/3}}\]
C.	\[9{{u}^{2}}\]
D.	\[{{u}^{4/3}}\]
Answer» C. \[9{{u}^{2}}\]

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If \[u={{({{x}^{2}}+{{y}^{2}}+{{z}^{2}})}^{3/2}}\], then \[{{\left( \frac{\partial u}{\partial x} \right)}^{2}}+{{\left( \frac{\partial u}{\partial y} \right)}^{2}}+{{\left( \frac{\partial u}{\partial z} \right)}^{2}}=\] [EAMCET 1996]

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