Find $\frac{dy}{dx}$ at $(5, 3)$ for the curve $x^2 - y^2 = 16$.

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: $\frac{dy}{dx} = \frac{x}{y}$.

3. 03

   At $(5, 3)$ this is $\frac{5}{3}$.