Prove that $\frac{dy}{dx} = -\frac1{(1+x)^2}$ for given that $x\sqrt{1+y} + y\sqrt{1+x} = 0$ $$x\sqrt{1+y} + y\sqrt{1+x} = 0$$

Please tell me where I went wrong. Why I am not getting correct answer ?

I see nothing wrong with your work....
Use the given equation in question in your result to simplify it further to get the required answer.
