How do you differentiate  f(x)=(ln(6x+8))^2 using the chain rule.?

Jun 3, 2016

I found: $f ' \left(x\right) = \frac{6}{3 x + 4} \ln \left(6 x + 8\right)$
First derive the ${\left(\right)}^{2}$ as it is then multiply by the derivative of the $\ln$ (red) and finally multply by the derivative of the argument of the $\ln$ (blue):
$f ' \left(x\right) = 2 {\left(\ln \left(6 x + 8\right)\right)}^{2 - 1} \cdot \textcolor{red}{\frac{1}{6 x + 8}} \cdot \textcolor{b l u e}{6} =$
$= \frac{12}{6 x + 8} \ln \left(6 x + 8\right) = \frac{12}{2 \left(3 x + 4\right)} \ln \left(6 x + 8\right) =$
$= \frac{6}{3 x + 4} \ln \left(6 x + 8\right)$