Answer
\[{y^,} = \frac{1}{{x\ln 6}}\]
Work Step by Step
\[\begin{gathered}
y = \log \,\left( {6x} \right) \hfill \\
Use\,\,\,the\,\,formula\,\,in\,\,the\,\,page\,\,238 \hfill \\
\frac{d}{{dx}}\,\,\left[ {{{\log }_a}\left| {g\,\left( x \right)} \right|} \right] = \frac{1}{{\ln a}}\frac{{{g^,}\,\left( x \right)}}{{g\,\left( x \right)}} \hfill \\
Then \hfill \\
{y^,} = \frac{1}{{\ln 6}}\,\,\left[ {\frac{{\,{{\left( {6x} \right)}^,}}}{{6x}}} \right] \hfill \\
Then \hfill \\
{y^,} = \frac{1}{{\ln 6}}\,\left( {\frac{6}{{6x}}} \right) \hfill \\
{y^,} = \frac{1}{{x\ln 6}} \hfill \\
\end{gathered} \]
