Higher order derivatives (look for a pattern)

If a question asks you to find a higher-order derivative, then we should differentiate the function a few times and look for a pattern. Of course, you should remember all the derivative techniques such as the power rule, product rule, quotient rule, and chain rule.
0:00 Q1 higher-order derivative of ln(x)
5:23 Q2 higher-order derivative of cos(x)
9:17 Q3 higher-order derivative of sin(2x)
13:02 Q4 higher-order derivative of sqrt(e^x)
15:36 Q5 higher-order derivative of x*e^x
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Just calculus.

[@yoav613]

Next challenge: find apattern(formula) for the integral (sinx)^n/x^n from 0 to inf

[@sokolovrasputin4081]

big kobe fan? 8, 24, 81, 1996, and 2016 are all pretty coincidental

[@bprpcalculusbasics]

Finally someone got it!

[@neuralwarp]

What is kobe?

[@thedudethatneveruploads2617]

@@neuralwarp i think its like a cheese, idk

[@ampisiades]

Thanks bprp for these free calc lessons.
The best way to spend my evenings.

[@anshumanagrawal346]

I see you've got Delta and Pi in your name, of course you like Math

[@aymanad3437]

@@anshumanagrawal346 lmao

[@fanamatakecick97]

Andrés Mpisiádhs (ik it’s pronounced Brisiádis) is a beautiful name

[@lordstevenson9619]

Perfect timing, I just started higher order derivatives in my lectures

[@hgthed570]

شكرا أنقذتني❤

[@fanamatakecick97]

This was enlightening

[@Shreyas_Jaiswal]

Do you know I can define n! (n factorial) as d^n(x^n)/dx^n. In simple word, nth derivative of x^n.

[@abhaychandra2624]

Thanks!!

[@shazi9883]

THANK YOU SO MUCH

[@vitalsbat2310]

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!

[@yoav613]

The last example is the easiest for achange!

[@yoav613]

This reminds me number theory with the order mod n and primitive root. Number theory calculus the order of cosx is 4😀

[@bprpcalculusbasics]

Yea 😆

[@Magnus-727]

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.

[@otesunki]

Some Calculus Behind 1/81 (8 years ago): ua-cam.com/video/xw4RBLjNUC8/v-deo.html
1/81, the pattern will surprise you!! (5 years ago): ua-cam.com/video/Hki5XoaZt3Y/v-deo.html
you combined two videos in your head

[@shubhammygt37]

Hi professor, I am from 🇮🇳

[@loandx2074]

Couldn't you also just say that dⁿ/dxⁿ(cos(x)) = cos(x+nπ/2) and dⁿ/dxⁿ(sin(2x)) = 2ⁿsin(x+nπ/2)

[@bprpcalculusbasics]

That’s is very nice!

[@rabahazzoug7323]

How can we calculate the nth derivitive of f=e^(x^2)

[@pneujai]

can we have a general chen lu for nth derivative

[@mathiasjeppesen6781]

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?

[@mathiasjeppesen6781]

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)

[@mathiasjeppesen6781]

And another one - the integral of e^ax * x^a dx = Γ(a + 1, -ax)/a^3 + C

[@mathiasjeppesen6781]

Btw - All natural numbers n.

[@StevenMRSenior]

For remainder can you use mod4?

[@rose.puddles]

Cool Poké Ball & Kirby too!

[@denischen8196]

What is the pattern for the nth derivative of tan(x)?

[@bprpcalculusbasics]

Lol I will pass on that.

[@michaelribeiro4818]

2 x 81 cos (2x)

[@andreas_bls]

Hello Franklin!

[@seroujghazarian6343]

Q1:-5040/x^8

[@anshumanagrawal346]

0:01
10/10

[@neuralwarp]

It would be more satisfying if you did a proper proof by induction.

[@pranavr488]

7:40 Dividing what by what ? I don't get it

[@bprpcalculusbasics]

Divide by 4

[@NonTwinBrothers]

Wait so did he like prerecord a bunch of these then only now upload them?

[@stevemonkey6666]

I was 34 years old in 1996. 😐

[@anshumanagrawal346]

Bruh

[@anshumanagrawal346]

You must be like 80 now

[@stevemonkey6666]

@@anshumanagrawal346 👽🇦🇺

[@williamcarver7590]

@@anshumanagrawal346 or 59

[@shubhammygt37]

I want to make a video in straight line.

[@sagargour2024]

Who

[@aydenherold443]

My Teacher: Now, what is the 100th derivative of sec(x)?

[@dqrksun]

find the 69th derivative of cosx+isinx with respect to i plspls

[@mrwiter4255]

It's 0

[@megauser8512]

lol that would be 0

[@royal_zaffreknightx3445]

It’s gonna be 0 and like why are you treating a number as a variable?

[@dqrksun]

@@royal_zaffreknightx3445 Just messin around xd

[@razaulkarim6091]

I found you through ALLAH,THanks(Shukriya) to ALLAH

[@lucarijoe8301]

Ok, now do non-integer derivatives :). Yeah, I know it doesn't make sense...