$\\frac{d}{dx}\\ln(3x)=\\frac{1}{3x}$. \ntrue \nfalse
$\\frac{d}{dx}\\ln(3x)=\\frac{1}{3x}$. \ntrue \nfalse
Answer
Explanation:
Step1: Apply chain - rule
Let $u = 3x$, then $y=\ln(u)$. The derivative of $y$ with respect to $u$ is $\frac{dy}{du}=\frac{1}{u}$, and the derivative of $u$ with respect to $x$ is $\frac{du}{dx}=3$. By the chain - rule $\frac{dy}{dx}=\frac{dy}{du}\cdot\frac{du}{dx}$.
Step2: Substitute and calculate
Substitute $u = 3x$, $\frac{dy}{du}=\frac{1}{u}$ and $\frac{du}{dx}=3$ into the chain - rule formula. We get $\frac{d}{dx}\ln(3x)=\frac{1}{u}\cdot3=\frac{1}{3x}\cdot3=\frac{1}{x}$.
Answer:
B. False