Derivatives of powers cotangent functions

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Find the derivative $\;\;\;\frac{d}{dx}cot^{5}(3x-8)$

**Answer**

$\;\;\;\frac{d}{dx}cot^{5}(3x-8)$

$=(5)\,cot^{4}(3x-8)\,(-csc^2(3x-8))\,(3)$

$=-15\,cot^{4}(3x-8)\,csc^2(3x-8)$