Differentiate `cos^(-1){sqrt((1+cosx)/(2))}` w.r.t. x.

Explanation

To differentiate the function \( y = \cos^{-1}\left(\sqrt{\frac{1 + \cos x}{2}}\right) \) with respect to \( x \), we will follow these steps:

### Step 1: Rewrite the function
Let:
\[ y = \cos^{-1}\left(\sqrt{\frac{1 + \cos x}{2}}\right) \]

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