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

Explanation

`y=cos ^{-1}{frac{x+sqrt{1-x^{2}}}{sqrt{2}}}`



Let `x=sin theta`

Now



`y=cos ^{-1}{frac{sin theta+sqrt{1-sin ^{2} theta}}{sqrt{2}}}`

Using `sin ^{2} theta+cos ^{2} theta=1`

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