In this video, I showed how to differentiate x^x^x^x
Пікірлер: 87
@ADWYETYATRIPATHYBEI7 ай бұрын
It's been 6 years since I opened a Math book... and this vid just brought back memories of school and college days!!! You deserve way more subscribers
@PrimeNewtons7 ай бұрын
Thank you!
@akiya92166 ай бұрын
The questions you do are normally quite easy for me and would be pretty boring to go through, but watching you do them is really enjoyable. Very very very fun, you are good at teaching :)
@PrimeNewtons6 ай бұрын
Maybe I'll step it up soon 🤣🤣🤣
@et427gamer97 ай бұрын
I am in algebra two so this all goes over my head but I still enjoy it significantly! Cant wait to get to higher level math like this. I can tell you love the subject and that love will transfer to your students. Keep it up!
@nengimotejaphet25659 күн бұрын
I usually feel shy watching your videos ’cause you’re so flirty😌😹 but this one! I can’t even lie you did this explanation better than organic chemistry tutor, and he was my go-to KZbin tutor! Guess who is my go-to KZbin tutor now🤭❤️
@cherryisripe31655 ай бұрын
Everything seems so simple with your explanations and pedagogy. Thank you so much.
@saiprasadpadhy68325 ай бұрын
The best maths channel I found till date, I'm so interested in learning all these
@rishichava3557 ай бұрын
Thank you, you explain everything extremely well and make math very enjoyable!
@nanasung27017 ай бұрын
thank you so much, i've been struggling with differentiation and i have a test tomorrow for it ♥️
@ThenSaidHeUntoThem2 ай бұрын
This is brilliantly done!
@ananthianandan5537 ай бұрын
I'm subscribing this channel, because you deserve for it
@arbenkellici38086 ай бұрын
You are amazing proffesor You might be an excellent Hollywood actor as well I dont know how many subscribers you have, but beleive me, you deserve a lot more
@justpassingbyy7 ай бұрын
Bruh, you have such a pleasant voice.
@ananthianandan5537 ай бұрын
You are literally awesome ❤
@kathieharine59826 ай бұрын
Excellent professor!
@sunil.shegaonkar15 ай бұрын
I have problem with the last term at 16:16, it does not account for X^x, this term is not in y' but factored out. This is a multiplier of the greater bracket. Factoring increases stack of 2 to 3, but greater bracket has x^x which has No term in y'. Rest is wonderful, I had no idea how to find derivative of 3 stacked function
@lukaskamin7555 ай бұрын
So cool, I'm from Ukraine and we learn maths with slightly different approaches, though, of course, math is the same, no doubt. I definitely enjoy your videos, with such a hillarious attitude, and perfect clear language (being non-native English speaker, I can totally understand everything
@gokubaianassauro45337 ай бұрын
Your channel is amazing. I'm from Brazil and you helped me a lot. thanks
@PrimeNewtons7 ай бұрын
Happy to hear that!
@pk27125 ай бұрын
Beautiful . I love your enthusiasm . I just subscribed .
@PrimeNewtons5 ай бұрын
Thanks for subbing!
@surendrakverma5553 ай бұрын
Very good. Thanks 🙏
@maeveoconnor8217 ай бұрын
Great video, it helped me so much!
@user-jo7nu2ur6n7 ай бұрын
Very good as usual 👍🏻
@Calcprof4 ай бұрын
If y = x^x^x^x^......, then y = x^y, and differentiate implicitly. and solve. This gives y' in terms of x, y, and log x. You have to be a little careful of boundary values, but I think you can handle these. BTW: y can be easily expressed in terms of the Lambert W function y = - W(-log[x])/log[x]. Since W'[x] = W[x]/(x (1 + W[x])), this can be used to calculate y' and express it entirely in terms of x, log[x] and W[x]. (You have to be a little careful of which branch of the solutions of z = x e^x you have, but all of this can be sorted out.)
@123qopsiznoq7 ай бұрын
Thank you
@mansourativo96587 ай бұрын
"Why am I not multiplying? Because I don't want to"😂 This is like me also sometimes when I teach my friends and classmates
@littlegrass3207 ай бұрын
how do you solve x^x^x = 3 using Lambert W function
@devcoachingclasses16 ай бұрын
Your 'Nice' word is very nice❤
@AS-ix3qd5 ай бұрын
nice work
@gghelis5 ай бұрын
Gotta integrate this now, just to check.
@kavvame3 ай бұрын
Thanks to find something to have good time
@samtube7613 күн бұрын
I am from ethiopia i always see your vidio
@user-xg1ch3zb8y2 ай бұрын
Thank you very much for opening my eyes, Professor! so much appreciate in your way to explain and solve that question quite easily. Well if I could ask you about what is the differentiate of X^X^X^2x, what is it should be then?
@jumpman82822 ай бұрын
Hi! The easiest way (in my opinion) to tackle this type of problem is to start by differentiating 𝑦 = 𝑥^(2𝑥). Taking the natural log of both sides, we get ln 𝑦 = 2𝑥 ln 𝑥. Implicit differentiation (chain rule on the left-hand side and product rule on the right) then gives us 1 ∕ 𝑦⋅𝑑𝑦 ∕𝑑𝑥 = 2⋅ln(𝑥) + 2x⋅1 ∕ 𝑥 = 2(ln(𝑥) + 1) (Note that we don't have to worry about 𝑥 = 0 in the denominator since 𝑥^(2𝑥) is not defined for 𝑥 = 0 anyway, so 𝑥 ∕ 𝑥 = 1) ⇒ 𝑑𝑦 ∕ 𝑑𝑥 = 𝑦⋅2(ln(𝑥) + 1) = 𝑥^(2𝑥)⋅2(ln(𝑥) + 1). So, 𝑑 ∕ 𝑑𝑥[𝑥^(2𝑥)] = 𝑥^(2𝑥)⋅2(ln(𝑥) + 1). - - - Now we can differentiate 𝑦 = 𝑥^𝑥^(2𝑥), using the exact same method. Take the natural log of both sides: ln 𝑦 = 𝑥^(2𝑥) ln 𝑥. Implicit differentiation: 1 ∕ 𝑦⋅𝑑𝑦 ∕ 𝑑𝑥 = 𝑑 ∕ 𝑑𝑥[𝑥^(2𝑥)]⋅ln(𝑥) + 𝑥^(2𝑥)⋅1 ∕ 𝑥 = 𝑥^(2𝑥)⋅2(ln(𝑥) + 1)⋅ln(𝑥) + 𝑥^(2𝑥)⋅1 ∕ 𝑥 = 𝑥^(2𝑥)⋅(2(ln²(𝑥) + ln 𝑥) + 1 ∕ 𝑥). ⇒ 𝑑𝑦 ∕ 𝑑𝑥 = 𝑦⋅𝑥^(2𝑥)⋅(2(ln²(𝑥) + ln 𝑥) + 1 ∕ 𝑥) = 𝑥^𝑥^(2𝑥)⋅𝑥^(2𝑥)⋅(2(ln²(𝑥) + ln 𝑥) + 1 ∕ 𝑥). So, 𝑑 ∕ 𝑑𝑥[𝑥^𝑥^(2𝑥)] = 𝑥^𝑥^(2𝑥)⋅𝑥^(2𝑥)⋅(2(ln²(𝑥) + ln 𝑥) + 1 ∕ 𝑥). - - - Finally, we can differentiate 𝑦 = 𝑥^𝑥^𝑥^(2𝑥). ln 𝑦 = x^𝑥^(2𝑥) ln 𝑥. 1 ∕ 𝑦⋅𝑑𝑦 ∕ 𝑑𝑥 = 𝑥^𝑥^(2𝑥)⋅𝑥^(2𝑥)⋅(2(ln²(𝑥) + ln 𝑥) + 1 ∕ 𝑥)⋅ln(𝑥) + 𝑥^𝑥^(2𝑥)⋅1 ∕ 𝑥 = 𝑥^𝑥^(2𝑥)⋅(𝑥^(2𝑥)⋅(2(ln³(𝑥) + ln²𝑥) + ln(𝑥) ∕ 𝑥) + 1 ∕ 𝑥) ⇒ 𝑑𝑦 ∕ 𝑑𝑥 = 𝑥^𝑥^𝑥^(2𝑥)⋅𝑥^𝑥^(2𝑥)⋅(𝑥^(2𝑥)⋅(2(ln³(𝑥) + ln²𝑥) + ln(𝑥) ∕ 𝑥) + 1 ∕ 𝑥). So, in the end we have 𝑑 ∕ 𝑑𝑥[𝑥^𝑥^𝑥^(2𝑥)] = 𝑥^𝑥^𝑥^(2𝑥)⋅𝑥^𝑥^(2𝑥)⋅(𝑥^(2𝑥)⋅(2(ln³(𝑥) + ln²𝑥) + ln(𝑥) ∕ 𝑥) + 1 ∕ 𝑥).
@gopikayala655112 күн бұрын
In general differentiation decrease the equation but in this case not applied
@OmChouhan-ps6sk4 ай бұрын
you have such a beautiful hat. from where did you get that?
@josephparrish76257 ай бұрын
That was fun! Where do you find these crazy problems? Lol
@PrimeNewtons7 ай бұрын
Lol. Usually, someone sends me a problem like this.
@Notking444.22 күн бұрын
Can you make full concept clearing video of differentiation
@luca_151Ай бұрын
would it be easier to say y = x*y, then ln y = y lnx, and then differentiate from there?
@gdubbsboi16407 ай бұрын
Have you done videos on factorials? Would love to learn it from you.
@PrimeNewtons5 ай бұрын
I think I'll do factorials soon
@roddos14 күн бұрын
Great hat.
@DSN.0015 ай бұрын
are tetrations derivatable?
@superiorjr1545 ай бұрын
At what point does differentiation turn into tetration or vice versa
@Deadpool-rw1pk7 ай бұрын
I am writing this question before watching the video : i guess you are going to use natural log (since it more convenient to derivative ) ?????
@user-vy6oc2cr5m5 ай бұрын
Differentiate x ^^ x (^^ means superpower like ³3 means 3^3^3)
@mehmetdurna31155 ай бұрын
Nice equation
@aaditya82837 ай бұрын
Sir can you plz bring a video pf proper explanation of why e^x differentiation and integration is e^x always bcz your explanation are easy to understand😊😊 love you from India.
@PrimeNewtons5 ай бұрын
I already have that
@souverain1erАй бұрын
@Prime Newtons Your thinking is as organized as your writing
@PrimeNewtonsАй бұрын
I hope that's a compliment because I'm still trying to organize my thinking 🤔
@wavingbuddy35355 ай бұрын
i tried this myself and got the same answer but i wrote mine as: x^( x^x^x + x^x + x) * ( ln(x)^3 + ln(x)^2 + ln(x)/x + 1/(x^(x+1))) very satisfying video as usual, love your charisma when you're going through the steps
@user-op6me3mr3w4 ай бұрын
Help me please🙏 I've a arcsin(1/3) and I need to find that, but I need an exact value. I mean I needn't a number like 0,3472.....I need an expression. For example: Arcsin(1/4(√5-1))=π/10 Arcsin(1/2)=π/6 Arcsin(1/3)=??? Arcsin(1/3)=?
@CRnk1537 ай бұрын
Hey, just saw your video about tetration, it would be x with 4 in left top corner
@first-namelast-name7 ай бұрын
GGEZW 😎
@jamesburrelljr.85616 ай бұрын
I like you but this is all above my head. I still gave you a Like.
@darcash17386 ай бұрын
After this I did it with 5 x’s above the original x. It barely fit in a single line 😂
@Yesandwhoareyou6 ай бұрын
How seductive
@lirich07 ай бұрын
Comment for the algorithm
@flowingafterglow6295 ай бұрын
You what would have been a really cool way to end that video would be to evaluate the derivative at some point (not x = 0 or 1, though). Something like, 2. This is the slope of the line x^x^x^x at x = 2..... It's a beautiful expression, but it's fun to remember a use of the derivative.... (maybe in the next video set y' = 0 and find critical points....)
@leoniii12477 ай бұрын
Woah this is way harder than I thought... I thought the answer was x^x^x^x * x^3 * ln(x) and I got no idea why the video is that long...😂
@luggis7574Ай бұрын
So many eggs 😂
@Alisdead5 ай бұрын
So, after need to find extremum of this :D
@beaverbuoy30117 ай бұрын
:D
@stew8805 ай бұрын
2:44 shouldn't 3^3^3 be 3^9 instead of 3^27
@pritamsur19264 ай бұрын
Sir please solve my indefinite integration:- integral of(32-x^5)^(1/5) dx
@jensberling23415 ай бұрын
Is there a mistake? You said 2^2^2=2^4. Then you said; 3^3^3=3^27. That must be a misprint. Pls, responds, Dr. Newton.
@jumpman82822 ай бұрын
A power tower is evaluated top down. However, some calculators interpret 3^3^3 as (3^3)^3 instead of 3^(3^3), so you've got to be careful.
@theupson5 ай бұрын
i know of no finesse for the actual labor of the problem, but the whole construction is more legible, maybe, if you start with y = s^t^u^v s=t=u=v=x and use multivariate chain rule. if that's out of bounds, switch the first three "x" for e^logx. y=exp(logx * exp (logx * exp (x*logx))) and the disassembly via chain rule and the product rule subtasks flows pretty naturally
@annxu82196 ай бұрын
if y=x x=1=y
@mikedubovs15747 ай бұрын
Had to click
@dellaih_studiesАй бұрын
Its a 11 th grade question😅
@prateek1.913 күн бұрын
this equation is a mosnter
@lec_hdАй бұрын
algo
@niom94467 ай бұрын
the step where you did x^(-1)-x^x=x^(-1-x) is wrong
@bhaskarporey37687 ай бұрын
He didn't....that's x^(-1)/x^x which is x^(-1-x) and it is correct.
@niom94467 ай бұрын
@@bhaskarporey3768oh right I didn’t see more. But he did write x^(-1)-x^x=x^(-1-x) though
@miscostsmusic18807 ай бұрын
@@bhaskarporey3768he did write the division sign, but the two dots were barely visible lmao
@owoLight5 ай бұрын
easy! dy/da = 0!
@dellaih_studiesАй бұрын
Who are here from cbse board😅
@christopherguerra72365 ай бұрын
No; not t, use u sub 2. LOL!!!
@PrimeNewtons5 ай бұрын
😀😀
@pabs-mugiwara7 ай бұрын
is thet ⁴x??? I just watched your video 'bout tetration (8 months ago), I really enjoyed it!