Differentiate the following function with respect to `x :` `sin^(-1){(sinx+cosx)/(sqrt(2))}`,`-(3pi)/4 lt xlt pi/4 `

Explanation

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

### Step 1: Rewrite the function
We start with the function:
\[ y = \sin^{-1}\left(\frac{\sin x + \cos x}{\sqrt{2}}\right) \]
We can rewrite the argument of the inverse sine function:
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