Differentiate the following function with respect to `x :` `sin^(-1){(x+sqrt(1-x^2))/(sqrt(2))}`,`-1 lt x lt1`

Explanation

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

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

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