A) 9u
B) \[9{{u}^{4/3}}\]
C) \[9{{u}^{2}}\]
D) \[{{u}^{4/3}}\]
Correct Answer: B
Solution :
\[\frac{\partial u}{\partial x}=\frac{3}{2}{{({{x}^{2}}+{{y}^{2}}+{{z}^{2}})}^{1/2}}.2x\] \[\therefore \]\[{{\left( \frac{\partial u}{\partial x} \right)}^{2}}=\frac{9}{4}({{x}^{2}}+{{y}^{2}}+{{z}^{2}})4{{x}^{2}}\]= \[9{{x}^{2}}({{x}^{2}}+{{y}^{2}}+{{z}^{2}})\] \[\therefore \]\[{{\left( \frac{\partial u}{\partial x} \right)}^{2}}+{{\left( \frac{\partial u}{\partial y} \right)}^{2}}+{{\left( \frac{\partial u}{\partial z} \right)}^{2}}\] = \[9\,({{x}^{2}}+{{y}^{2}}+{{z}^{2}})\,({{x}^{2}}+{{y}^{2}}+{{z}^{2}})\] = \[9\,{{({{x}^{2}}+{{y}^{2}}+{{z}^{2}})}^{2}}\] = \[9.{{u}^{4/3}}\].
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