question_answer

If \[Z=si{{n}^{-1}}\left( \frac{x+y}{\sqrt{x}+\sqrt{y}} \right),\] then \[x\frac{\partial z}{\partial x}+y\frac{\partial z}{\partial y}\] is equal to

A)  \[\frac{1}{2}\sin Z\]                  

B)  \[\frac{1}{2}\tan Z\]

C)  0                                

D)  \[\frac{1}{2}\]

E)  None of these