Find `(dy)/(dx)" for "y=sin^(-1) (cos x), x in (0, pi)cup (pi, 2pi).`

Explanation

To find \(\frac{dy}{dx}\) for the function \(y = \sin^{-1}(\cos x)\) where \(x\) lies in the intervals \((0, \pi)\) and \((\pi, 2\pi)\), we can simplify the expression before differentiating. Here’s a step-by-step solution:

### Step 1: Simplify the Function
We know that:
\[ \cos x = \sin\left(\frac{\pi}{2} - x\right) \]
Thus, we can rewrite \(y\) as:
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