If $z = \sin^{-1} \{ \frac{x+y}{\sqrt{x} + \sqrt{y} } \}$, then $x \frac{\partial z}{\partial x} + y \frac{\partial z}{\partial y}$ is equal to :

Question

( A ) $\cot z$
( B ) $\frac{1}{2} \cot z$
( C ) $\tan z$
( D ) $\frac{1}{2} \tan z$