Derivative of ln(sin(x)), chain rule with natural log and sine. #shorts

Derivative of ln(sin(x)), chain rule with natural log and sine.

In order to differentiate ln(sin(x)), we view it as a function composition with sin(x) as the inner function and ln(x) as the outer function. We then differentiate ln(sin(x)) with respect to sin(x), giving us 1/sin(x). The chain rule requires us to tack on the derivative of sin(x), giving us an extra factor of cos(x), and finally we express the final answer as cot(x).