Derivatives of powers secant functions

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Find the derivative $\;\;\;\frac{d}{dx}sec^{9}(x-1)$

**Answer**

$\;\;\;\frac{d}{dx}sec^{9}(x-1)$

$=(9)\,sec^{8}(x-1)\,(sec(x-1)\,tan(x-1))\,(1)$

$=9\,sec^{9}(x-1)\,tan(x-1)$