If \[z={{\sin }^{-1}}\left( \frac{x+y}{\sqrt{x}+\sqrt{y}} \right)\], then \[x\frac{\partial z}{\partial x}+y\frac{\partial z}{\partial y}\] is equal to [EAMCET 1998; Orissa JEE 2000]

If \[z={{\sin }^{-1}}\left( \frac{x+y}{\sqrt{x}+\sqrt{y}} \right)\], t

1.	If \[z={{\sin }^{-1}}\left( \frac{x+y}{\sqrt{x}+\sqrt{y}} \right)\], then \[x\frac{\partial z}{\partial x}+y\frac{\partial z}{\partial y}\] is equal to [EAMCET 1998; Orissa JEE 2000]
A.	\[\frac{1}{2}\sin z\]
B.	\[\frac{1}{2}\tan z\]
C.	\[0\]
D.	None of these
Answer» C. \[0\]

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If \[z={{\sin }^{-1}}\left( \frac{x+y}{\sqrt{x}+\sqrt{y}} \right)\], then \[x\frac{\partial z}{\partial x}+y\frac{\partial z}{\partial y}\] is equal to [EAMCET 1998; Orissa JEE 2000]

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