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My Summer of Math Exposition 5 entry: "This is not the second derivative"
This is not the second derivative. My submission to this year's SoME5.
In the Leibniz notation, we write differentials as fractions. But can we really treat them as such? While it works for the first derivative, it breaks down already for the second. In this video, we find out why and rebuild the second derivative with the product rule, so that it behaves like an algebraic object. As a bonus, we arrive at the second-order inversion formula in a few steps.
This video is based on the paper “Extending the Algebraic Manipulability of Differentials” by Bartlett & Khurshudyan (2018).
u/Splinesd — 4 days ago