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

Explanation

`"We have "xsqrt(1+y)+ysqrt(1+x)=0`
`"or "xsqrt(1+y)=-ysqrt(1+x)`
`"or "x^(2)(1+y)=y^(2)(1+x)" [On squaring both sides]"`
`"or "x^(2)-y^(2)=y^(2)x-x^(2)y`
`"or "(x+y)(x-y)=-xy(x-y)`
`"or "x+y=-xy" "[because x- yne 0" as "x = y" does not satisfy the given equation"]`
`"or "y=-(x)/(1+x)`
`"or "(dy)/(dx)=-{((1+x)xx1-x(0+1))/((1+x^(2)))}=-(1)/((1+x^(2)))`