x^3 + y^3 = 1
please explain step by step thnx
$\displaystyle \frac{d}{dx}(x^3+y^3)=\frac{d}{dx}(1)$
Key point:: y is a function of x so we have to use the chain rule
$\displaystyle \frac{d}{dx}x^3+\frac{d}{dx}y^3=\frac{d}{dx}(1)$
$\displaystyle 3x^2+3y^2\frac{dy}{dx}=0 \iff 3y^2\frac{dy}{dx}=-3x^2 \iff \frac{dy}{dx}=-\frac{x^2}{y^2}$