Differentiate the following w.r.t x
`cos^(-1) (sqrt(1+x//2))`

Explanation

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

### Step 1: Identify the outer function and the inner function
Here, the outer function is \( \cos^{-1}(u) \) where \( u = \sqrt{\frac{1+x}{2}} \).

### Step 2: Differentiate the outer function
The derivative of \( \cos^{-1}(u) \) with respect to \( u \) is given by:
\[
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