In this video we derive both curvature formulas from the basic definition of what curvature is. Curvature is the rate of change of the unit tangent vector with respect to arclength. The first curvature formulas derivation starts with that definition. The second curvature formulas derivation is much less intuitive, but it is a great exercise in keeping track of useful things we know or can show. I hope this video helps clear up from where both curvature formulas arise. Thanks for watching! -dr. Dub