What is the correct way to solve this? Explain in steps. Thank you.

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1 Answer
Sep 23, 2017

Use chain rule

Explanation:

#f(x) = u/v#
#f'(x) = (vdu-udv)/v^2#

Use this relationship to compute the derivative

#u = (1+sqrt(3x))# and #v = (1-sqrt(3x))#
#du = sqrt(3)/(2sqrt(x))#
#dv = -sqrt(3)/(2sqrt(x))#

#f'(x)=(((1-sqrt(3x))sqrt(3))/(2sqrt(x))+((1+sqrt(3x))sqrt(3))/(2sqrt(x)))/(1-sqrt(3x))^2#

-#f'(x) =(sqrt(3)(1-\cancel(sqrt(3x))+1+\cancel(sqrt(3x))))/(2sqrt(x)(1-sqrt(3x))^2#

#f'(x) =3/(sqrt(3x)(1-sqrt(3x))^2#