#### Answer

\[{y^,} = \frac{2}{{\,{{\left( {1 - t} \right)}^2}}}\]

#### Work Step by Step

\[\begin{gathered}
y = \frac{{9 - 7t}}{{1 - t}} \hfill \\
Use\,\,the\,\,quotient\,\,rule\,\,to\,\,find\,\,{y^,}\, \hfill \\
{y^,}\, = \frac{{\,\left( {1 - t} \right)\,{{\left( {9 - 7t} \right)}^,} - \,\left( {9 - 7t} \right)\,{{\left( {1 - t} \right)}^,}}}{{\,{{\left( {1 - t} \right)}^2}}} \hfill \\
Then \hfill \\
{y^,} = \frac{{\,\,\left( {1 - t} \right)\,\left( { - 7} \right) - \,\left( {9 - 7t} \right)\,\left( { - 1} \right)}}{{\,\,{{\left( {1 - t} \right)}^2}}} \hfill \\
Simplify\,\,by\,\,multiplying\,\,and\,\,combining\,\,terms \hfill \\
{y^,} = \frac{{ - 7 + 7t - 7t + 9}}{{\,{{\left( {1 - t} \right)}^2}}} \hfill \\
{y^,} = \frac{2}{{\,{{\left( {1 - t} \right)}^2}}} \hfill \\
\end{gathered} \]