[cidyah]

1) Product rule:
y=xe^(3-x)csc(2x)
dy/dx = e^(3-x)csc(2x) +x e^(3-x)(-1)csc(2x) - x e^(3-x) csc(2x)cot(2x)(2)
dy/dx = e^(3-x)csc(2x)-xe^(3-x)csc(2x)-2x e^(3-x) csc(2x)cot(2x)

2)The denominator is incorrect.