Find `(dy)/(dx)` for `y=sin^(-1)(cosx),` where `x in (0,2pi)dot`

Explanation

To find \(\frac{dy}{dx}\) for the function \(y = \sin^{-1}(\cos x)\), we will follow these steps:

### Step 1: Differentiate using the chain rule
We start with the function:
\[ y = \sin^{-1}(\cos x) \]
To differentiate \(y\) with respect to \(x\), we apply the chain rule. The derivative of \(\sin^{-1}(u)\) with respect to \(u\) is:
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