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

Explanation

To solve the problem, we start with the equation given:

\[ x \sqrt{1+y} + y \sqrt{1+x} = 0 \]

We need to differentiate this equation implicitly with respect to \(x\) to find \(\frac{dy}{dx}\).

...