Question

How do you differentiate `f(x)=sqrt((1-x)/(1+x))`?

Answer 1

`f'(x)=x/((1+x)sqrt(1-x^2))`

Explanation:

`f(x)=sqrt(1-x)/sqrt(1+x)`
By applying quotient rule,
Let `u=sqrt(1-x)` and
`v=sqrt(1+x)`
`f'(x)=(u'v-v'u)//v^2`
`f'(x)={1/2root(-1/2)(1-x)*sqrt(1+x)-1/2root(-1/2)(1+x)*sqrt(1-x)}/(1+x)`
`f'(x)=1/2{(sqrt(1+x)/sqrt(1-x))-(sqrt(1-x)/sqrt(1+x)}//(1+x)`
`f'(x)=1/2{1+x-1+x}/((1+x)sqrt(1-x^2))`
`f'(x)=x/((1+x)sqrt(1-x^2))`