Differentiate the function. f(x) = ln(225 sin^2 x)

Differentiate the function.
f(x) = ln(225 sin^2 x)

Thanks!

First, you can simplify f(x) using logarithm rules to get:
f(x) = ln[225sin^2(x)]
= ln(225) + ln[sin^2(x)], since ln(ab) = ln(a) + ln(b)
= ln(225) + 2ln[sin(x)], since ln(a^b) = b*ln(a).

Then, differentiating using the Chain Rule yields:
f'(x) = 0 + 2cos(x)/sin(x) = 2cot(x).

I hope this helps!