#### Answer

\[y'' = 2{\csc ^2}x\cot x\]

#### Work Step by Step

\[\begin{gathered}
y = \cot x \hfill \\
\hfill \\
differentiate\,\,to\,\,find\,\,y{\,^,} \hfill \\
\hfill \\
\frac{{dy}}{{dx}} = - {\csc ^2}x \hfill \\
\hfill \\
find\,\,\,y{\,^{,\,}} \hfill \\
\hfill \\
y'' = - 2\left( {\csc x\,\,} \right)\,{\left( {\csc x} \right)^\prime } \hfill \\
\hfill \\
differentiate\,\,to\,\,find\,\,{y^,}^, \hfill \\
use\,\,the\,\,product\,\,rule \hfill \\
\hfill \\
y'' = - 2\,\left( {\csc x} \right)\,\left( { - \csc x\cot x} \right) \hfill \\
\hfill \\
simplify \hfill \\
\hfill \\
y'' = 2{\csc ^2}x\cot x \hfill \\
\end{gathered} \]