Integrals are used to find the average of a continuous variable, and this can offer a perspective on why integrals and derivatives are inverses, distinct from the one shown in the last video.
Implicit differentiation can feel weird, but what's going on makes much more sense once you view each side of the equation as a two-variable function, f(x, y).
Derivatives center on the idea of change in an instant, but change happens across time while an instant consists of just one moment. How does that work?
In this first video of the series, we see how unraveling the nuances of a simple geometry question can lead to integrals, derivatives, and the fundamental theorem of calculus.