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

Explanation

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

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

### Step 1: Rearranging the Equation
We can rearrange the equation to isolate one of the terms:
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