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

1 Answer
mizoo
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)#

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