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