An old (1986) BBC documentary on The birth of the calculus, presented by Jeremy Gray of the Open University and author of the recent book Plato’s Ghost: The modernist transformation of mathematics. I believe this is part of the course MA290, “Topics in the History of Mathematics”.
Around three minutes in we learn of a pre-Newtonian trick for finding the tangent to a curve — find the osculating circle, draw its radius (which is normal to the curve), and then the tangent is perpendicular to it. This was unfamiliar to me. Much of the history will be familiar to many, but there’s always the novelty of seeing (video of) Newton’s actual papers. As you may have heard, Cambridge has recently digitized many of Newton’s papers. Though the video is British, it shows some of Leibniz’ papers too, including the one where he introduces the integral sign.
The same youtube channel has videos of a few In our time podcasts from BBC Radio 4, which I cannot account for because they are just audio with a static picture on top, but they may be interesting content. (I haven’t listened.)