Derivatives of powers cosecant functions

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Find the derivative $\;\;\;\frac{d}{dx}csc^{3}(4x+1)$

**Answer**

$\;\;\;\frac{d}{dx}csc^{3}(4x+1)$

$=(3)\,csc^{2}\,(4x+1)\,(-csc(4x+1)\,cot(4x+1))\,(4)$

$=-12\,csc^{3}(4x+1)\,cot(4x+1)$