If `xsqrt(1+y)+ysqrt(1+x)=0,` prove that `(dy)/(dx)=-1/((x+1)^2)`

Explanation

\begin{equation}
\begin{aligned}
&x \sqrt{1+y}+y \sqrt{1+x}=0\\
&x \sqrt{1+y}=-y \sqrt{1+x}\\
&x^{2} \cdot(1+y)=(-y)^{2} \cdot(1+x)\\
&x^{2} \cdot(1+y)=y^{2} \cdot(1+x)\\
&x^{2}+x^{2} \cdot y=y^{2}+y^{2} \cdot x\\
&x^{2}-y^{2}=y^{2} \cdot x-x^{2} \cdot y\\
...