## What is the derivative of ln 3x?

Answer:

\(\frac{d y}{d x}=\frac{1}{x}\)

Explanation:

We will need the standard result:

By the rule of logs:

\(\begin{aligned}

y &=\ln 3 x \\

&=\ln 3+\ln x

\end{aligned}\).

Or we can implicitly apply the chain rule:

\(\frac{d y}{d x}=\frac{1}{3 x} \cdot 3=\frac{1}{x}\)