Differentiate `sqrt((1-x)/(1+x))` with respect to x.

Explanation

Let y=`sqrt((1-x)/(1+x))=((1/x)/(1+x))^(1//2)`
`rArrlogy=log((1-x)/(1+x))^(1//2)=1/2log((1-x)/(1+x))`
`=1/2[log(1-x)-log(1+x)]`
Differentiate both sides with respect to x
`1/y(dy)/(dx)=1/2[(-1)/(1-x)-1/(1+x)]`
`=1/2[(-1-x-1+x)/(1-x^(2))]=(-1)/(1-x^(2))`
`rArr(dy)/(dx)=-y/(1-x^(2))=-1/(1-x^(2))sqrt((1-x)/(1+x))`
`=(-1)/((1+x)^(1//2)(1+x)^(3//2))` Ans.