I don't think I got the numbers right but I noticed a few things: Question 1-4: The number (8, 24, 81 and 1996) is divisible by the question number. It just doesn't match with 2016 in question 5. For the 81: I remember you did a video on 1/81 and it's "missing" 8's a long time ago. It could be in 2013 which is 8 years ago.
Some Calculus Behind 1/81 (8 years ago): th-cam.com/video/xw4RBLjNUC8/w-d-xo.html 1/81, the pattern will surprise you!! (5 years ago): th-cam.com/video/Hki5XoaZt3Y/w-d-xo.html you combined two videos in your head
I’ve found a pattern for the integral of ln^n(x) dx. The integral of ln^n(x) is equal to the sum from k = 0 to n of ((-1)^k * ln^(n-k) * n!/(n-k)!).. Tho I haven’t really proven why this is the case for all n. Can anyone help me with that?
Same with the integral of ln^n(x)*x^m dx. The integral of ln^n(x)*x^m is equal to the sum from k = 0 to n of (x^(m+1)/(m+1)^(k+1) * ln^(n-k) * n!/(n-k)! * (-1)^k)
Next challenge: find apattern(formula) for the integral (sinx)^n/x^n from 0 to inf
Thanks bprp for these free calc lessons.
The best way to spend my evenings.
I see you've got Delta and Pi in your name, of course you like Math
@@anshumanagrawal346 lmao
Andrés Mpisiádhs (ik it’s pronounced Brisiádis) is a beautiful name
big kobe fan? 8, 24, 81, 1996, and 2016 are all pretty coincidental
Finally someone got it!
What is kobe?
@@neuralwarp i think its like a cheese, idk
Perfect timing, I just started higher order derivatives in my lectures
The last example is the easiest for achange!
Do you know I can define n! (n factorial) as d^n(x^n)/dx^n. In simple word, nth derivative of x^n.
I don't think I got the numbers right but I noticed a few things:
Question 1-4: The number (8, 24, 81 and 1996) is divisible by the question number. It just doesn't match with 2016 in question 5.
For the 81: I remember you did a video on 1/81 and it's "missing" 8's a long time ago. It could be in 2013 which is 8 years ago.
Some Calculus Behind 1/81 (8 years ago): th-cam.com/video/xw4RBLjNUC8/w-d-xo.html
1/81, the pattern will surprise you!! (5 years ago): th-cam.com/video/Hki5XoaZt3Y/w-d-xo.html
you combined two videos in your head
This reminds me number theory with the order mod n and primitive root. Number theory calculus the order of cosx is 4😀
Yea 😆
شكرا أنقذتني❤
2 x 81 cos (2x)
Q1:-5040/x^8
Hi professor, I am from 🇮🇳
I’ve found a pattern for the integral of ln^n(x) dx. The integral of ln^n(x) is equal to the sum from k = 0 to n of ((-1)^k * ln^(n-k) * n!/(n-k)!).. Tho I haven’t really proven why this is the case for all n. Can anyone help me with that?
Same with the integral of ln^n(x)*x^m dx. The integral of ln^n(x)*x^m is equal to the sum from k = 0 to n of (x^(m+1)/(m+1)^(k+1) * ln^(n-k) * n!/(n-k)! * (-1)^k)
And another one - the integral of e^ax * x^a dx = Γ(a + 1, -ax)/a^3 + C
Btw - All natural numbers n.
THANK YOU SO MUCH
0:01
10/10
Couldn't you also just say that dⁿ/dxⁿ(cos(x)) = cos(x+nπ/2) and dⁿ/dxⁿ(sin(2x)) = 2ⁿsin(x+nπ/2)
That’s is very nice!
This was enlightening
hi bprp, i wanna ask is there a f(x) with dn/dxn f(x) = (x+n)e^(x+n) ? please answer. thanks for the video!
Cool Poké Ball & Kirby too!
What is the pattern for the nth derivative of tan(x)?
Lol I will pass on that.
Thanks!!
How can we calculate the nth derivitive of f=e^(x^2)
Hello Franklin!
It would be more satisfying if you did a proper proof by induction.
For remainder can you use mod4?
can we have a general chen lu for nth derivative
I was 34 years old in 1996. 😐
Bruh
You must be like 80 now
@@anshumanagrawal346 👽🇦🇺
@@anshumanagrawal346 or 59
Wait so did he like prerecord a bunch of these then only now upload them?
I want to make a video in straight line.
Who
7:40 Dividing what by what ? I don't get it
Divide by 4
I found you through ALLAH,THanks(Shukriya) to ALLAH
My Teacher: Now, what is the 100th derivative of sec(x)?
find the 69th derivative of cosx+isinx with respect to i plspls
It's 0
lol that would be 0
It’s gonna be 0 and like why are you treating a number as a variable?
@@royal_zaffreknightx3445 Just messin around xd
Ok, now do non-integer derivatives :). Yeah, I know it doesn't make sense...