Differentiate the following with respect to x
`cos^(-1) sqrt((1+cosx)/2)`

Explanation

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

### Step 1: Rewrite the expression using the half-angle formula
We know from trigonometric identities that:
\[ 1 + \cos x = 2 \cos^2 \left( \frac{x}{2} \right) \]
Substituting this into the expression, we have:
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