If $$u = \sin^{-1} \frac{x + y}{\sqrt{x} + \sqrt{y}}$$ then by Euler’s theorem, $$x. \frac{\partial u}{\partial x}+y .\frac{\partial u}{\partial y}$$ will be

A

$$\frac{1}{2} \sin u$$

B

$$\frac{1}{2} \tan u$$

C

$$x + y$$

D

$$\sin x + \sin y$$