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

1 Answer
Mar 18, 2018

-(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)