#### Answer

\[{y^,} = \frac{{8x - 9}}{{4{x^2} - 9x}}\]

#### Work Step by Step

\[\begin{gathered}
y = \ln \left| {4{x^2} - 9x} \right| \hfill \\
Find\,\,the\,\,derivative \hfill \\
{y^,} = \,\,\left[ {\ln \,\left| {4{x^2} - 9x} \right|} \right] \hfill \\
Use\,\,the\,\,formula\,\,\frac{d}{{dx}}\,\,\left[ {\ln g\,\left( x \right)} \right] = \frac{{{g^,}\,\left( x \right)}}{{g\,\left( x \right)}} \hfill \\
Here\,\,g\,\left( x \right) = 4{x^2} - 9x \hfill \\
Then \hfill \\
{y^,} = \frac{{\,{{\left( {4{x^2} - 9x} \right)}^,}}}{{4{x^2} - 9x}} \hfill \\
Differentiating \hfill \\
{y^,} = \frac{{8x - 9}}{{4{x^2} - 9x}} \hfill \\
\end{gathered} \]