Find $\frac{dy}{dx}$ at $(2, 4)$ for the curve $x^3 + y^3 = 9xy$.

Explanation

1. 01

   Differentiate every term with respect to $x$, treating $y$ as a function of $x$, so $y$ terms pick up $\frac{dy}{dx}$.

2. 02

   Solving for it: $\frac{dy}{dx} = \frac{x^{2} - 3 y}{3 x - y^{2}}$.

3. 03

   At $(2, 4)$ this is $\frac{4}{5}$.