#### Answer

\[{y^,} = \,\,\frac{4}{{\,\left( {4x - 3} \right)\ln 10}}\]

#### Work Step by Step

\[\begin{gathered}
y = \log \,\left( {4x - 3} \right) \hfill \\
Differentiate \hfill \\
{y^,} = \,\,{\left[ {\log \,\left( {4x - 3} \right)} \right]^,} \hfill \\
Use\,\,the\,\,formula \hfill \\
\frac{d}{{dx}}\,\,\left[ {{{\log }_a}\left| {g\,\left( x \right)} \right|} \right] = \frac{1}{{\ln a}} \cdot \frac{{{g^,}\,\left( x \right)}}{{g\,\left( x \right)}} \hfill \\
Here\,\,\,g\,\left( x \right) = 4x - 3\,\,,\,\,a = 10 \hfill \\
Then \hfill \\
{y^,} = \frac{1}{{\ln 10}}\,\left( {\frac{{\,{{\left( {4x - 3} \right)}^,}}}{{4x - 3}}} \right)\,\, \hfill \\
{y^,} = \,\,\frac{1}{{\ln 10}}\,\left( {\frac{4}{{4x - 3}}} \right) \hfill \\
{y^,} = \,\,\frac{4}{{\,\left( {4x - 3} \right)\ln 10}} \hfill \\
\end{gathered} \]