y = ln|csc(x)| Find the derivative of the function.

y=ln|csc(x)|
To take the derivative of this, use the formula:
(ln u)' = 1/u*u'
Applying that, y' will be:
y'=1/(cscx)*(cscx)'
Take note that the derivative of cosecant is (csctheta)' = -cscthetacottheta .
y'=1/cscx*(-cscxcotx)
y'=-cotx
 
Therefore, the derivative of the given function is y'=-cotx .