You’ve provided the function:

$f(x) = \ln(\cos x)$

Would you like me to find its derivative, explore its domain, or perform a different analysis? Let me know how you would like to proceed!

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Here are 5 follow-up questions to expand the topic:

1. What is the derivative of $f(x) = \ln(\cos x)$?
2. What is the domain of $f(x) = \ln(\cos x)$?
3. How does $f(x) = \ln(\cos x)$ behave as $x$ approaches specific values (like $\pi/2$ or 0)?
4. What is the integral of $f(x) = \ln(\cos x)$?
5. How does the graph of $f(x) = \ln(\cos x)$ compare to the graph of $\cos x$?

Tip: Remember, the domain of $\ln(x)$ is restricted to $x > 0$, so for $f(x) = \ln(\cos x)$, $\cos x$ must be positive!