Differentiate `sin^(-1)[(sqrt(1+x)+sqrt(1-x))/2]` with respect to 'x'.

Explanation

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

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

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