Answer
\[{y^,} = \frac{1}{{\,\left( {\ln 3} \right)x}}\]
Work Step by Step
\[\begin{gathered}
y = \log \,\left| {3x} \right| \hfill \\
Find\,\,the\,\,derivative \hfill \\
{y^,} = \,\,\,{\left[ {\log \,\left| {3x} \right|} \right]^,} \hfill \\
Use\,\,the\,\,formula \hfill \\
\frac{d}{{dx}}\,\,\left[ {{{\log }_a}\left| {g\,\left( x \right)} \right|} \right] = \frac{1}{{\ln a}} \cdot \frac{{{g^,}\,\left( x \right)}}{{g\,\left( x \right)}} \hfill \\
Here\,\,\,g\,\left( x \right) = 3x,\,\,a = 10 \hfill \\
Then \hfill \\
{y^,} = \,\frac{1}{{\ln 3}}\,\left( {\,\frac{{\,{{\left( {3x} \right)}^,}}}{{3x}}} \right) \hfill \\
{y^,} = \frac{1}{{\ln 3}}\,\left( {\frac{3}{{3x}}} \right) \hfill \\
Simplifying \hfill \\
{y^,} = \frac{1}{{\,\left( {\ln 3} \right)x}} \hfill \\
\end{gathered} \]
