Question

Find $\frac{dy}{dx}$ of $x^2+xy+y^2=100$

Answer 1

$x^2+xy+y^2=100$
Differentiating both sides w.r.t $x$ we get,
$\frac{d}{dx}(x^2+xy+y^2)=\frac{d}{dx}\left(100\right)=0$
$\Rightarrow 2x+y.1+x.\frac{dy}{dx}+2y\frac{dy}{dx}=0$
$\Rightarrow 2x+y+(x+2y)\frac{dy}{dx}=0$
$\therefore \frac{dy}{dx}=-\frac{2x+y}{x+2y}$