#### Answer

\[\frac{{dy}}{{dx}} = \frac{{7x}}{{4y}}\]

#### Work Step by Step

\[\begin{gathered}
7{x^2} - 4{y^2} = 24 \hfill \\
\,Find\,\,dy/dx\,\,\,by\,\,implicit\,\,differentiation \hfill \\
\frac{{dx}}{{dy}}\,\left( {7{x^2} - 4{y^2}} \right) = \frac{d}{{dx}}\,\left( {24} \right) \hfill \\
7\,\left( 2 \right){x^{2 - 1}} - 4\,\left( 2 \right){y^{2 - 1}}{y^,} = 0 \hfill \\
14x - 8y{y^,} = 0 \hfill \\
- 8y{y^,} = - 14x \hfill \\
Divide\,\,by\,\, - 8y \hfill \\
{y^,} = \frac{{ - 14x}}{{ - 8y}} = \frac{{7x}}{{4y}} \hfill \\
Then \hfill \\
\frac{{dy}}{{dx}} = \frac{{7x}}{{4y}} \hfill \\
\end{gathered} \]