pi-th derivative of x^pi

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Here we will see how to find the pi-th derivative of x^pi. It's part of "fractional calculus". enjoy!

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Bro thats sounds like d^3/dx^3(x^3) with extra steps

juakoncio

That's one of those things that just looks absolutely impossible, but someone's solving it for 9 minutes.

newwaveinfantry

I just found out that
Gamma(pi + 1) = 7.1880827...

chirayu_jain

Just the video-title on its own managed to make me feel really anxious. I am glad we physicists don't see things like that so often :D

JustHoldIt

5:18 how can you just write ...3*2*1 at the end there? if the whole point is that 'a' is not necessarily an integer, then (a-n) is not necessarily an integer, so it may never hit 3*2*1.

nathanisbored

This is one thing that is really cool about math;
you can take something that is somewhat intuitive (derivatives are reasonably intuitive, since they are kind of like extreme cases of the point-slop formula), and then expand on that and show that it works for much more general situations.

Peter_

Just finished out differential equations today. I just want to thank you for helping me through it. At the beginning of this semester I commented on one of your videos that it was a shame you didn’t have any videos for diffy q, but then you directed me to your playlists and boy did those videos (along with Patrick JMT) save me in that class.

You two youtubers helped me through my entire math career.

Thank you.

whoami

How do you even interpret the pi-th derivative geometrically?

GottfriedLeibnizYT

Got out of surgery a few hours ago, so I was very happy to see a new video from you in my recommended. Nice work :D

MacheTheFerret

You should be having a billion subscribers coz studying Mathematics with you is really really Fun, love these kinda videos, Fantastic work sir!

Infinite_Precision

What's the motivation behind the expanding of the definition of derivative into the real number order?

broccoloodle

I think u r the only teacher who makes me so curious about maths

hotshot

I really appreciate your channel, it's entertaining, educational, impressive, and unlike some people, you don't belittle minorities in the process! Thank you for making this videos, I appreciate you

evelynmisaki

According to the fundamental theorem of engineering, I got 6.

matthewpoynter

Sir you relate your videos pretty well!

aaryansrivastava

Always cool and great extension of my HS maths.

paulfaigl

This is a nice heuristic argument, but would be better by introducing the fractional operator as an integral transform and going from there to get Gamma(pi + 1).

adandap

An intro like this should be included in calc 1 getting students to know derivatives is not just integer but it can take fractional derivative and can be think of as a function operated on an equation

ekueh

"at the end we'll get a really nice answer"
later at the end: "~2.188"
I truly was hoping that you'll show an exact answer like e^(pi/4) or something

omerresnikoff

Hi! At 5:52 how do you make sure a<n<0? Otherwise it isn't a factorial at all...

anthonygreven

pi-th derivative of x^pi

pi-th derivative of x^pi

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