`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` .**

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`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` .**