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

Explanation

Solution:

`-1
`u=\cos ^{-1} \sqrt{\frac{1+\cos 2 \theta}{2}}=\cos ^{-1} \sqrt{\frac{2 \cos ^{2} \theta}{x^{-}}}`

`u=\cos ^{-1}(\cos \theta)=\theta`

`2 \theta=\cos ^{-1} x \Rightarrow \theta=\frac{1}{2} \cos ^{-1} x`

`u=\frac{1}{2} \cos ^{-1} x`

`[du]/[dx]=-1/2sqrt(1-x^2)`