#### Answer

\[{y^,} = \frac{1}{x}\]

#### Work Step by Step

\[\begin{gathered}
y = \ln \,\left( { - 4x} \right) \hfill \\
Find\,\,the\,\,derivative \hfill \\
{y^,} = \,\,\left[ {\ln \,\left( { - 4x} \right)} \right] \hfill \\
Use\,\,the\,\,formula\,\,\frac{d}{{dx}}\,\,\left[ {\ln g\,\left( x \right)} \right] = \frac{{{g^,}\,\left( x \right)}}{{g\,\left( x \right)}} \hfill \\
Here\,\,g\,\left( x \right) = - 4x\, \hfill \\
Then \hfill \\
{y^,} = \frac{{\,{{\left( { - 4x} \right)}^,}}}{{ - 4x}} \hfill \\
{y^,} = \frac{{ - 4}}{{ - 4x}} \hfill \\
simplifying \hfill \\
{y^,} = \frac{1}{x} \hfill \\
\end{gathered} \]