Complex derivatives can be difficult to grasp, they are not just a simple slope of a tangent on a curve. But with polar curves, and a bit of trickery in how we express them, they become unexpectedly intuitive.
Secret Kinks of Elementary Functions:
https://youtu.be/92wXQYcYLMg
Derivatives of Polar Functions (standard method):
https://math24.net/derivatives-polar-functions.html
Math3D Butterfly:
https://www.math3d.org/2IMQVqBfs
Music by:
@Lisayamusic