Derivatives of powers cotangent functions

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Find the derivative $\;\;\;\frac{d}{dx}cot^{7}(x+6)$

**Answer**

$\;\;\;\frac{d}{dx}cot^{7}(x+6)$

$=(7)\,cot^{6}(x+6)\,(-csc^2(x+6))\,(1)$

$=-7\,cot^{6}(x+6)\,csc^2(x+6)$