Answer
\[{f^,}\,\left( x \right) = \frac{{101}}{{\,{{\left( {7x + 3} \right)}^2}}}\]
Work Step by Step
\[\begin{gathered}
f\,\left( x \right) = \frac{{8x - 11}}{{7x + 3}} \hfill \\
Use\,\,the\,\,quotient\,\,rule\,\,to\,\,find\,\,{f^,}\,\left( x \right) \hfill \\
{f^,}\,\left( x \right) = \frac{{\,\left( {7x + 3} \right)\,\,{{\left( {8x - 11} \right)}^,} - \,\left( {8x - 11} \right){{\left( {7x + 3} \right)}^,}}}{{{{\left( {7x + 3} \right)}^2}}} \hfill \\
Then \hfill \\
{f^,}\,\left( x \right) = \frac{{\left( {7x + 3} \right)\,\left( 8 \right) - \,\left( {8x - 11} \right)\,\left( 7 \right)}}{{{{\left( {7x + 3} \right)}^2}}} \hfill \\
Simplify\,\,by\,\,multiplying\,\,and\,\,combining\,\,terms \hfill \\
{f^,}\,\left( x \right) = \frac{{56x + 18 - 56x + 77}}{{\,{{\left( {7x + 3} \right)}^2}}} \hfill \\
{f^,}\,\left( x \right) = \frac{{101}}{{\,{{\left( {7x + 3} \right)}^2}}} \hfill \\
\hfill \\
\end{gathered} \]
