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

Jun 24, 2016

$\frac{6 \left(x + 1\right)}{3 {x}^{2} + 6 x + 5}$
$f \left(x\right) = \ln \left(3 {x}^{2} + 6 x + 5\right)$
as a general matter if $y = \ln \left(f \left(x\right)\right)$ then $y ' = \frac{1}{f \left(x\right)} f ' \left(x\right)$ [chain rule]
here $f ' \left(x\right) = \frac{1}{3 {x}^{2} + 6 x + 5} \left(3 {x}^{2} + 6 x + 5\right) '$
$= \frac{6 x + 6}{3 {x}^{2} + 6 x + 5}$