Question

first use appropriate properties of logarithms to rewrite f(x), and then find f(x). f(x)=\ln(\frac{4}{x}) f(x)=\square

Explanation:

Step1: Use logarithm property

Recall $\ln(\frac{a}{b})=\ln(a)-\ln(b)$. So, $f(x)=\ln(4)-\ln(x)$.

Step2: Differentiate term - by - term

The derivative of a constant $\ln(4)$ is $0$, and the derivative of $\ln(x)$ is $\frac{1}{x}$. Using the difference rule of differentiation $(u - v)'=u'-v'$, where $u = \ln(4)$ and $v=\ln(x)$. So $f'(x)=0-\frac{1}{x}=-\frac{1}{x}$.

Answer:

$-\frac{1}{x}$