first use appropriate properties of logarithms to rewrite f(x), and then find f’(x).\nf(x)=ln(7/x)\nf’(x)=□
first use appropriate properties of logarithms to rewrite f(x), and then find f’(x).\nf(x)=ln(7/x)\nf’(x)=□
Answer
Explanation:
Step1: Use logarithm property
Recall $\ln(\frac{a}{b})=\ln(a)-\ln(b)$. So, $f(x)=\ln(7)-\ln(x)$.
Step2: Differentiate term - by - term
The derivative of a constant $\ln(7)$ is $0$, and the derivative of $\ln(x)$ is $\frac{1}{x}$. Using the difference rule of differentiation $(u - v)'=u'-v'$, where $u = \ln(7)$ and $v=\ln(x)$. Then $f'(x)=0-\frac{1}{x}=-\frac{1}{x}$.
Answer:
$-\frac{1}{x}$