A curve is given by $x = t - \frac{1}{t}$, $y = t + \frac{1}{t}$. What is its slope $\frac{dy}{dx}$ at $t = 2$?

Explanation

1. 01

   $\frac{dx}{dt} = 1 + \frac{1}{t^{2}}$ and $\frac{dy}{dt} = 1 - \frac{1}{t^{2}}$.

2. 02

   $\frac{dy}{dx} = \frac{dy/dt}{dx/dt} = \frac{t^{2} - 1}{t^{2} + 1}$.

3. 03

   At $t = 2$ the slope is $\frac{3}{5}$.