Differentiate `cos^(-1){(x+sqrt(1-x^2))/(sqrt(2))},\ -1

Explanation

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

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

### Step 2: Use trigonometric identities
We can express the argument of the inverse cosine in terms of sine. Notice that:
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