Solution
= Solution
<Implicit differentiation> yields $3y^2y'+2x=0$. At $x=1$, the real curve has $y^3=1$, hence $y=1$. Therefore
$$
\boxed{\left.\frac{dy}{dx}\right|_{(1,1)}=-\frac23.}
$$
= Solution
<Implicit differentiation> yields $3y^2y'+2x=0$. At $x=1$, the real curve has $y^3=1$, hence $y=1$. Therefore
$$
\boxed{\left.\frac{dy}{dx}\right|_{(1,1)}=-\frac23.}
$$