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