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

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\( x \sqrt{1+y}+y \sqrt{1+x}=0 \), then \( \frac{d y}{d x}= \)
\( \mathrm{P} \)
(A) \( 1+x \)
(B) \( (1+x)^{-2} \)
(C) \( -(1+x)^{-1} \)
(D) \( -(1+x)^{-2} \)
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