How do you find the derivative of #ln(x/3)#?

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Answer 1 · 2017-01-26T08:01:01

#1/x#

method 1
use the chain rule

#(dy)/(dx)=(dy)/(du)xx(du)/(dx)#

#y=ln(x/3)#

#u=x/3=>(du)/(dx)=1/3#

#y=lnu=>(dy)/(du)=1/u#

#:.(dy)/(dx)=1/uxx1/3=1/(x/3)xx1/3#

#:.(dy)/(dx)=3/x xx1/3=1/x#

method 2

use rules of logs

#y=ln(x/3)=lnx-ln3#

#(dy)/(dx)=d/(dx)(lnx)-d/(dx)(ln3)#

#=1/x-0=1/x#