17/03/2026
Howdy Fellas!
We’ve all spent hours grinding through the nth derivative of a function, but have you ever stopped to wonder what happens if n isn’t a whole number? It sounds like a glitch in the matrix, but "half derivatives" are actually a real thing that change the way we look at calculus.
By using the Gamma function to stretch factorials into the world of decimals, we can calculate derivatives for values like 0.5 or 0.75. Unlike the normal derivatives you’re used to, these are "non-local," meaning the value at a single point actually depends on the entire history of the function.
It even turns out that solving the mystery of the Tautochrone curve, where an object falls in the same amount of time regardless of height is as simple as taking a half derivative.
If you want to see how we go from basic integrals to the math that breaks the traditional rules of calculus, check out the post!
