Answer
\[{y^,} = - \frac{{6x}}{{5y}}\]
Work Step by Step
\[\begin{gathered}
6{x^2} + 5{y^2} = 36 \hfill \\
\,Find\,\,the\,\,implicit\,\,differentiation \hfill \\
\frac{d}{{dx}}\,\left( {6{x^2} + 5{y^2}} \right) = \frac{d}{{dx}}\,\left( {36} \right) \hfill \\
6\,\left( 2 \right){x^{2 - 1}} + 5\,\left( 2 \right){y^{2 - 1}}{y^,} = 0 \hfill \\
12x + 10y{y^,} = 0 \hfill \\
10y{y^,} = - 12x \hfill \\
Divide\,\,by\,\,10y \hfill \\
{y^,} = - \frac{{12x}}{{10y}} \hfill \\
{y^,} = - \frac{{6x}}{{5y}} \hfill \\
\hfill \\
\end{gathered} \]
