Question

let
$f(x)=2\ln(6x)$
$f(x)=\square$
$f(2)=\square$
question help: video

Explanation:

Step1: Apply chain - rule

The derivative of $\ln(u)$ is $\frac{u'}{u}$. Here $u = 6x$, so $u'=6$. And we have a coefficient of 2. So $f'(x)=2\times\frac{6}{6x}$.

Step2: Simplify $f'(x)$

$f'(x)=\frac{12}{6x}=\frac{2}{x}$.

Step3: Evaluate $f'(2)$

Substitute $x = 2$ into $f'(x)$. So $f'(2)=\frac{2}{2}=1$.

Answer:

$f'(x)=\frac{2}{x}$
$f'(2)=1$