If \(x \sqrt{1+y}+y \sqrt{1+x}=0\), then \(\frac{d y}{d x}=\)

1
\(\frac{-1}{(1+x)^2}\)
2
\(\frac{1}{(1+x)^2}\)
3
\(\frac{2}{(1+x)^{3 / 2}}\)
4
\(\frac{-2}{(1+x)^{1 / 2}}\)

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