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)
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