#### Answer

\[{f^,}\,\left( x \right) = 2\sqrt 2 {x^{\sqrt 2 - 1}}\]

#### Work Step by Step

\[\begin{gathered}
f\,\left( x \right) = 2{x^{\sqrt 2 }} \hfill \\
\hfill \\
using\,\,the\,\,power\,\,rule \hfill \\
\hfill \\
{f^,}\,\left( x \right) = n{x^{n - 1}} \hfill \\
\hfill \\
then \hfill \\
\hfill \\
{f^,}\,\left( x \right) = 2\sqrt 2 {x^{\sqrt 2 - 1}} \hfill \\
\hfill \\
\end{gathered} \]