Using the :

##d/dx(csc^2(x)) = d/dxu^2 d/dxu##, and ##u = csc(x), du = 2u##

##= 2csc(x) d/dx(cscx)##

##= -cot(x)csc(x)2csc(x)##

Simplying yields:

##=-2cot(x)csc^2(x)##