How do you find the derivative of $f(x)=ln(3x^(2)+6x+5)$ ?

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Answer 1 · 2016-06-24T11:59:33

$(6(x+1))/(3x^(2)+6x+5)$

$f(x)=ln(3x^(2)+6x+5)$

as a general matter if $y = ln ( f(x) )$ then $y' = 1/(f(x)) f'(x)$ [chain rule]

here $f'(x)=1/(3x^(2)+6x+5)(3x^(2)+6x+5)'$
$=(6x+6)/(3x^(2)+6x+5)$

How do you find the derivative of f(x)=ln(3x^(2)+6x+5)f(x)=ln(3x^(2)+6x+5)?