If `y=tan^(-1){(sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x))},"f i n d"(dy)/(dx)`

Explanation

Let`x=cos2theta=2cos^2theta-1`

`y=tan^(-1)((sqrt(1+cos2theta)-sqrt(1-cos2theta))/(sqrt(1+cos2theta)+sqrt(1-cos2theta)))`

`y=tan^(-1)((sqrt2costheta-sqrt2sintheta)/(sqrt2costheta-sqrt2sintheta))`

`y=tan^(-1)((1-tantheta)/(1+tantheta))`

`y=pi/4-theta=pi/4-1/2cos^(-1)x`

`dy/dx=-1/2-1/sqrt(1-x^2)=1/(2sqrt(1-x^2))`.