Find $\frac{\mathrm{d}y}{\mathrm{d}x}$ of $\ln(x^2+xy+y^2)=1$.
So for this natural log should I start by using the power rule or the the product rule of $xy$? The textbook talks about taking the natural log from both sides.
2026-03-29 10:16:42.1774779402
Implicit differentiation of $\ln(x^2+xy+y^2)=1$
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Exponentiate both sides of the equation to get that $$x^2+xy+y^2=e$$Take the derivative with respect to $x$: $$2x+y+xy'+2yy'=0$$Solve for $y'$ to get $$y'=-\frac{2x+y}{2y+x}$$
Note: I know the question doesn't follow community standards, but this is a new user who should be given a chance. I'm saying this just in case someone comments me to not answer low-quality questions.