#### Answer

\[{s^,} = \frac{{\,\left( {\ln 3} \right)\,\left( {{3^{\sqrt t }}} \right)}}{{\sqrt t }}\]

#### Work Step by Step

\[\begin{gathered}
s = 2 \cdot {3^{\sqrt t }} \hfill \\
Find\,\,the\,\,derivative \hfill \\
{s^,} = \,\,\,{\left[ {2 \cdot {3^{\sqrt t }}} \right]^,} \hfill \\
Pull\,\,out\,\,the\,\,constant\,\,2 \hfill \\
{s^,} = 2\,\,{\left[ {{3^{\sqrt t }}} \right]^,} \hfill \\
Use\,\,the\,\,formula \hfill \\
\frac{d}{{dx}}\,\,\left[ {{a^{g\,\left( x \right)}}} \right] = \,\left( {\ln a} \right){a^{g\,\left( x \right)}}{g^,}\,\left( x \right) \hfill \\
Then \hfill \\
{s^,} = 2\,\left( {\ln 3} \right)\,\left( {{3^{\sqrt t }}} \right)\,{\left( {\sqrt t } \right)^,} \hfill \\
Differentiate \hfill \\
{s^,} = 2\,\left( {\ln 3} \right)\,1\left( {{3^{\sqrt t }}} \right)\,\left( {\frac{1}{{2\sqrt t }}} \right) \hfill \\
{s^,} = \frac{{\,\left( {\ln 3} \right)\,\left( {{3^{\sqrt t }}} \right)}}{{\sqrt t }} \hfill \\
\end{gathered} \]