#### Answer

\[{s^,} = \frac{{5\ln 2\,\left( {{2^{\sqrt {t - 2} }}} \right)}}{{2\sqrt {t - 2} }}\]

#### Work Step by Step

\[\begin{gathered}
s = 5 \cdot {2^{\sqrt {t - 2} }} \hfill \\
Find\,\,the\,\,derivative \hfill \\
{s^,} = \,\,\,{\left[ {5 \cdot {2^{\sqrt {t - 2} }}} \right]^,} \hfill \\
Pull\,\,out\,\,the\,\,constant\,\,5 \hfill \\
{s^,} = 5\,\,{\left[ {{2^{\sqrt {t - 2} }}} \right]^,} \hfill \\
Use\,\,the\,\,formula \hfill \\
\frac{d}{{dx}}\,\,\left[ {{a^{g\,\left( x \right)}}} \right] = \,\left( {\ln a} \right){a^{g\,\left( x \right)}}{g^,}\,\left( x \right) \hfill \\
Then \hfill \\
{s^,} = 5\,\left( {\ln 2} \right)\,\left( {{2^{\sqrt {t - 2} }}} \right)\,{\left( {\sqrt {t - 2} } \right)^,} \hfill \\
differentiating\,\,\sqrt {t - 2} \hfill \\
{s^,} = 5\,\left( {\ln 2} \right)\,\left( {{2^{\sqrt {t - 2} }}} \right)\,\,\left( {\frac{1}{{2\sqrt {t - 2} }}} \right) \hfill \\
Multiply \hfill \\
{s^,} = \frac{{5\ln 2\,\left( {{2^{\sqrt {t - 2} }}} \right)}}{{2\sqrt {t - 2} }} \hfill \\
\end{gathered} \]