Question

Find $\frac{dy}{dx}$, if $x^3+y^2+xy=10$

Answer 1

$x^3+y^3+xy=10$

$\Rightarrow 3x^2+3y^2\frac{dy}{dx}+x\frac{dy}{dx}+y=0$ by differentiating w.r.t $x$

$\Rightarrow (3y^2+x)\frac{dy}{dx}=-(3x^2+y)$

$\Rightarrow \frac{dy}{dx}=\frac{-(3x^2+y)}{(3y^2+x)}$