If $x = \cos^3 t$ and $y = \sin^3 t$, what is $\frac{dy}{dx}$?

Explanation

1. 01

   $\frac{dx}{dt} = -3\cos^2 t\sin t$ and $\frac{dy}{dt} = 3\sin^2 t\cos t$.

2. 02

   $\frac{dy}{dx} = \frac{3\sin^2 t\cos t}{-3\cos^2 t\sin t} = -\frac{\sin t}{\cos t} = -\tan t$.