Answer
\[\frac{{dy}}{{dx}} = \frac{{5y - 8x}}{{3y - 5x}}\]
Work Step by Step
\[\begin{gathered}
8{x^2} - 10xy + 3{y^2} = 26 \hfill \\
\,Find\,\,dy/dx\,\,\,by\,\,implicit\,\,differentiation \hfill \\
\frac{d}{{dx}}\,\left( {8{x^2} - 10xy + 3{y^2}} \right) = \frac{d}{{dx}}\,\left( {26} \right) \hfill \\
Use\,\,the\,\,product\,\,rule\,\,for\,\,\frac{d}{{dx}}\,\left( {10xy} \right) \hfill \\
16x - 10\,\left( {x{y^,} + y\,\left( 1 \right)} \right) + 6y{y^,} = 0 \hfill \\
Multiplying \hfill \\
16x - 10x{y^,} - 10y + 6y{y^,} = 0 \hfill \\
Move\,\,all\,\,{y^,}\,\,to\,\,the\,\,same\,\,side\,\,of\,\,the\,\,equation \hfill \\
- 10x{y^,} + 6y{y^,} = 10y - 16x \hfill \\
Factor \hfill \\
{y^,}\,\left( { - 10x + 6y} \right) = 10y - 16x \hfill \\
{y^,} = \frac{{10y - 16x}}{{6y - 10x}} \hfill \\
Then \hfill \\
\frac{{dy}}{{dx}} = \frac{{5y - 8x}}{{3y - 5x}} \hfill \\
\end{gathered} \]
