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

Explanation

`xsqrt(1+y)+ysqrt(1+x)=0`

`xsqrt(1+y)=-ysqrt(1+x)`

`x^2(1+y)=y^2(1+x)`

`x^2+x^2y-y^2-xy^2=0`

`x^2-y^2+x^2y-xy^2=0`

`(x-y)(x+y)+xy(x-y)=0`

`(x-y)[x+y+xy]=0`

`x+y+xy=0`

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