If y=cos(3x)cosec(4x), find dy/dx.

Use the product rule: Let   u = cos3x ,     v = cosec4x Then du/dx = -3sin3x , dv/dx = -4cosec4xcot4x  (standard result, given in the formula booklet) Hence dy/dx = -4cosec4xcot4xcos3x - 3sin3xcosec4x . (No simplification required as it was not asked for in the question)