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

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

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

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