Question

How do you differentiate `sqrt((x+1)/(2x-1))`?

Answer 1

`-(3(x+1))/(2(2x-1)^2 sqrt((x+1)/(2x-1))`

Explanation:

`f(x) = u^n`
`f'(x) = n xx (du)/dx xxu^(n-1)`

In this case:`sqrt((x+1)/(2x-1))= ((x+1)/(2x-1))^(1/2):`
`n = 1/2, u = (x+1)/(2x-1)`

`d/dx = 1/2 xx (1xx(2x-1) - 2xx(x+1))/(2x-1)^2 xx ((x+1)/(2x-1))^(1/2-1)`

`= 1/2xx(-3)/((2x-1)^2 xx ((x+1)/(2x-1))^(1/2-1)`

`= -(3(x+1))/(2(2x-1)^2 ((x+1)/(2x-1))^(1/2)`