First, read Newton and Leibniz Develop Calculus. This is the Newton–Leibniz story that sets the stage: a curve can have a slope at a single instant. How do you measure change at a single instant when everything is moving? That question leads to a powerful new way of seeing curves.
Watch the 3Blue1Brown video Open:paradox of the derivative | Chapter 2, Essence of calculus where a secant line slides and becomes a tangent line. That “zooming in” is the whole secret. In this video, you’ll explore a surprising question: how can a curve have a slope at just one single point? By zooming in closer and closer, you’ll see that curves begin to look straight, revealing a well-defined slope called the instantaneous rate of change. As you watch, focus on how this idea helps us understand motion at an exact moment — the key to defining velocity in calculus.
Capture how fast something is changing at just one moment. See how the tangent line represents the instantaneous rate of change.
Pick two points close together, compute rise/run, then make them even closer. The slope you’re chasing is exactly what the tangent line captures.