Question #f3133

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Answer 1 · 2016-07-23T11:58:32

#= 2/x#

#d/dx( ln f(x) ) = 1/(f(x)) f'(x)#

So here that means

#d/dx( ln 3x^2 ) qquad star#

#= 1/(3x^2) * 6x#

#= 2/x#

Just to play about a bit, we can re-write #star# as

#d/dx( 2ln sqrt 3 x ) #

#= 2* 1/(sqrt 3 x) * sqrt 3 #

#= 2/x#

or we can rewrite #star# as

#d/dx( ln 3 + ln x^2 ) #

#= d/dx( ln 3 + 2 ln x ) #

#= 0 + 2 * 1/ x = 2/x #