Answer
$\csc x$
Work Step by Step
$\frac{d}{dx}\ln(\csc x-\cot x)$
$=\frac{1}{\csc x-\cot x}*\frac{d}{dx}(\csc x-\cot x)$
$=\frac{1}{\csc x-\cot x}*(-\csc x\cot x-(-\csc^2 x))$
$=\frac{1}{\csc x-\cot x}*(-\csc x\cot x+\csc^2 x)$
$=\frac{1}{\csc x-\cot x}*\csc x*(\csc x-\cot x)$
$=\csc x$
