Answer:
cot(x)
Explanation:
[tex]\frac{d}{dx}ln(sin(x))[/tex]
Use u-substitution,
[tex]u=sin(x)\\u'=cos(x)[/tex]
[tex]\frac{d}{dx}ln(sin(x)) = \frac{d}{du}ln(u)[/tex]
[tex]= \frac{1}{u}u'[/tex] //using the chain rule
[tex]= \frac{1}{sin(x)}cos(x)[/tex]
[tex]=cot(x)[/tex]
