What rules would I be using to solve this problem, and how would I use the differentials to find the derivative?
$\text{Find } dy/dx\colon x^{2}-4xy+y^2 = 4.$
2026-03-29 00:06:49.1774742809
How would I use differentials to solve this problem?
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If $$ x^2-4xy+y^2=4 $$ then applying the derivative operator $d$ we have $$ 2xdx-4xdy-4ydx+2ydy=0\implies xdx-2xdy-2ydx+ydy=0\\ \implies x-2x\frac{dy}{dx}-2y+y\frac{dy}{dx}=0\\ \implies \frac{dy}{dx}=\frac{2y-x}{y-2x} $$ Where we solved for the term $\frac{dy}{dx}$ treating the above symbols as differentials.