Yesterday I saw a video exploring fractional derivatives. That is, derivatives not of fractional exponents, but derivatives of functions midway between the first and second derivative, second and third, and so on. This topic got me thinking about how one goes about finding the nth derivative of a power function, which led me to write this little series of proofs. While I’m sure not original, all the work below is my own. It will hopefully allow me to explore the concept of fractional derivatives in more depth going forward. Taking an aside from my study of real analysis has been somewhat painful, though, so I think I’ll return to that for the time being.
Though I have done my best to proof-read these arguments, if you notice any issues with my work please send me an email at tyler@functionaltutoring.com. There are a few quirks in here that I haven’t properly vetted as of yet, but it’s a work in progress.
Tommy Benjamin 