Find \( \frac{d y}{d x} \) for \( y=\sin ^{-1}(\cos x) \), where \( x \in(0,2 \pi) \).

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Find \( \frac{d y}{d x} \) for \( y=\sin ^{-1}(\cos x) \), where \( x \in(0,2 \pi) \).
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