Answer:
[tex]\frac{dy}{dx} = \frac{8y - 2x}{2y - 8x}[/tex]
Step-by-step explanation:
The denominator is always the variable that we want to find the derivation in relation of. So it is always dx.
The number is the variable we derivated. So
[tex]x^{2} - 8xy + y^{2} = 8[/tex]
[tex]2x\frac{dx}{dx} - 8y\frac{dx}{dx} - 8x\frac{dy}{dx} + 2y\frac{dy}{dx} = 0[/tex]
[tex]2x - 8y + (2y - 8x)\frac{dy}{dx} = 0[/tex]
[tex](2y - 8x)\frac{dy}{dx} = 8y - 2x[/tex]
[tex]\frac{dy}{dx} = \frac{8y - 2x}{2y - 8x}[/tex]