Derivatives of cosecant functions

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Find the derivative $\;\;\;\frac{d}{dx}csc\left(5x+1\right)$

**Answer**

$\;\;\;\frac{d}{dx}csc\left(5x+1\right)$

$=-5\,csc\left(5x+1\right)\,cot\left(5x+1\right)$