Answer
$y''$ = $2csc^{2}(3x-1)cot(3x-1)$
Work Step by Step
$y$ = $\frac{1}{9}$$cot(3x-1)$
$y'$ = $\frac{d}{dx}$[$\frac{1}{9}$$cot(3x-1)$]
$y'$ = $\frac{1}{9}$$(-csc^{2}(3x-1))$ $\frac{d}{dx}$$(3x-1)$
$y'$ = $\frac{1}{9}$$(-csc^{2}(3x-1))$$(3)$
$y'$ = $-\frac{1}{3}$$csc^{2}(3x-1)$
$y''$ = $\frac{d}{dx}$[$-\frac{1}{3}$$csc^{2}(3x-1)$]
$y''$ = $-\frac{1}{3}$$2csc(3x-1)$ $\frac{d}{dx}$$(csc(3x-1))$
$y''$ = $[-\frac{2}{3}$$csc(3x-1)]$$[-csc(3x-1)cot(3x-1)]$ $\frac{d}{dx}$$(3x-1)$
$y''$ = $[-\frac{2}{3}$$csc(3x-1)]$$[-csc(3x-1)cot(3x-1)]$$(3)$
$y''$ = $2csc^{2}(3x-1)cot(3x-1)$
