`cos^(-1)((sqrt(1+x)-sqrt(1-x))/(2))`

Explanation

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

### Step 1: Simplify the Expression
Let \( x = \cos(\theta) \). Then we can rewrite the expression inside the inverse cosine function:
\[ y = \cos^{-1}\left(\frac{\sqrt{1+\cos(\theta)} - \sqrt{1-\cos(\theta)}}{2}\right) \]

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