I praise thy holy salaman kotal khan for his great work in the field of mathamatics. Without his holy butttery voice, I would be but a mere padwan of what I am today
@naziasiddiqui8807
3 жыл бұрын
U play mortal kombat
@Kervvy
3 жыл бұрын
@@naziasiddiqui8807 U play DN
@Fish-vs6jf
4 жыл бұрын
This left me far more confused than when I started
@montvmontv117
4 жыл бұрын
my prof said with chain rule to always say "the derivative of the outside times the derivative of the inside" it may make sense. so (stuff)^2 derivative is 2*(stuff) then take derivative of stuff. so 2(stuff) * stuff ' here sin would be cos. 2sin * cos
@priyankaboopathi729
4 жыл бұрын
Exactly.. 😥
@Saurabh_Tewari007
4 жыл бұрын
Well it cleared my doubt even though he wasn't really teaching
@aimzf20
4 жыл бұрын
MonTV MonTV this cleared it up so much for me, thank you!!!
@sudhamajayanthi
3 жыл бұрын
@@montvmontv117 I understood nothing but “stuff” 😶
@EastSideGameGuy
6 жыл бұрын
I sometimes come here to listen to his voice ._. it's soothing makes math Beautiful
@bonafidecatlover3443
3 жыл бұрын
Coming here for the first time and I can already see this man having a wave of fangirls
@Jorge-125
3 жыл бұрын
Everyone in the comments talking about math stuff while I'm over here trying to count how many times he said respectively. I'm just over here thinking how much respect is in this video.
@lidestudios5094
Жыл бұрын
I only watched this to review, I already know how the chain rule works, but the way he explained it makes it look more complicated than “derivative of outside when x= inside function, times derivative of the inside”
@MatthewReader
8 ай бұрын
Any good videos that you thought were a better review?
@thanaa6401
3 ай бұрын
He just doesn't want us to memorize it thats why he took harder approach
@josuequintero-td5gh
23 күн бұрын
Yeah because he's trying to make you understand why it works. Otherwise you're just memorizing formulas without knowing what they do.
@chawza8402
4 жыл бұрын
oh my god! my teacher taught me this but never mentioned it's called chain rule. I blindly use this method without knowing what it is for!
@nafy2302
3 жыл бұрын
What is wrong with your teacher
@p.c2750
4 жыл бұрын
What is the problem with some college/university teachers. is it laziness? I guess it is pride - it seems they dont want subjects to appear simple, too simple for students to suddenly catch what they spent many years to train for. It is not only right, but an honest thing to "call a spade a spade." Thanks KA!
@abhilashmishra5397
3 жыл бұрын
this video just saved me from failing in Physics. Thanks a lot Sal sir
@chrisfreilich
2 жыл бұрын
Still trying to figure out EXACTLY what 'with respect to' means. People always seem to gloss over it or talk around it.
@AFCA-vn9bl
Жыл бұрын
If you differentiate x^2 + y^2 with respect to x you will get 2x while differentiating with respect to y gives 2y
@thanaa6401
3 ай бұрын
It's just that you want to find the derivative (i.e. slope of the curve y = f(x)) AT the point x So whatever the point x on the line x squared, it's derivative will be 2 times this point ( i. e. 2x) When I want the derivative of x squared with respect to sinx. I mean this: whatever that point x is, I'm gonna find its sine. the specific value of this sine, I will input it into x squared and see what will be tge slope of line on THAT value. So, I take x, I input it into sin function, I get an output, I input this new output into the x squared function, I get a brand new output, and I want the slope of the line on that specific brand new output. I encourage you to watch composite functions videos from precalculus playlist + revise the intro videos on derivative as a concept
@satwikshourya2199
3 ай бұрын
It means that how does one value change with respect to another meaning , how much y will change if x is changed, for example if you derive postion x with respect to time t, then you get velocity meaning that derivative of x with respect to t is v, so when t has changed a little how much did x change or rather by factor did x change, that factor in this case is velocity v
@BoZhaoengineering
4 жыл бұрын
This planet needs you! Thank you for the learning videos!
@Jcava5
4 жыл бұрын
sorry, i feel like you shouldn't have used sin x, and instead just a simpler function. ive learned and understood the chain rule before and came here for a refresher and this didnt help :(
@jamessanpedro223
3 жыл бұрын
(x+y)^2
@PenandPaperScience
3 жыл бұрын
Or ln(x^2), like I solve step-by-step in my newest video. It might help you understand :)
@rajingajadhar4135
2 жыл бұрын
Found this channel in grade 12, and I'm coming back to it now in my final year (hopefully) of uni.
@OppenheimerUpandcoming
2 ай бұрын
OMG I FINALLY UNDERSTOOD THIS THING THANK U SO MUCH
@ernstboyd8745
27 күн бұрын
in the case of a linear function (where the function is just multiplying x by a constant) the derivative is just the product of the two derivatives. if f(x) = 5x and g(x) = 10x. then. g(f(x)) = 50x. and (50x)' =. f'(x) * g'(x) = 50 if the outer function is not linear like g(x) = x^2 then the slope changes depending on the input it gets from the inner function f this is why the slope of the g(x) should be evaluated at the same value as it gets from f(x) in other words. (g(f(x)))' = f'(x) *. g'(f(x))
@Syntaxxed
5 ай бұрын
all those hours in school vs a 5 min yt video... it keeps happening but I keep being amazed
@Yue27s
Жыл бұрын
wow super thanks mr.Khan kumar, now i really understand with this thing called chain rule how it work, but still cant visualized it but thanks i clearly know how it works now
@oferzilberman5049
4 жыл бұрын
I didn't quite understand what does it mean "With respect to something", And quora and google didn't really help, Can someone help me on this? Edit: I figured it out and it turns out it just means it's the x axis but now it can be substitued as other variables like t, So when it's "with respect to something" it means that the y equation is using that variable as the x
@alyssamanwarren8321
4 жыл бұрын
i don’t either
@Jorge-125
3 жыл бұрын
He's paying his respects to the math gods.... Jk, people always use that term and I still don't know why.
@PenandPaperScience
3 жыл бұрын
I just uploaded a video where I go through such exercises step-by-step, explaining everything along the way. It might help you. Regarding your question, take this example. 1. The derivative with respect to x of the function x^2 is 2x. 2. The derivative with respect to x of (x+3)^2 needs the chain rule to be solve. 3. The derivative with respect to (x+3) of (x+3)^2 is 2(x+3)
@anooby
2 ай бұрын
dang that actually made sense thx sal
@qualquan
2 жыл бұрын
The U substitution of inner x terms is simpler 2nd step is finding dU by differentiating U = dU/dx to express everything in x terms So 2 successive differentiations. "Outer and "inner"" Final result expressed as a differential coeff (DC) as a rule
@SUMANKARANTH-u8y
8 ай бұрын
The power/chain rule is the saviour of math
@hloniphalisa4632
5 жыл бұрын
I love you so much ,So wish you could be my math lecturer. you are better tan him. thank you so much I was thinking o changing my course but now never all your video you make math easy and simply
@issac1071
4 жыл бұрын
Hello, thank you so much for the video, but I have a question please: did the last notation was really treated as a fraction? Regards.
@aimzf20
4 жыл бұрын
No, it’s not a fraction. However, the way he write the notation can help you to think about the derivatives. They’re not fractions, however it may help you to think about them ‘cancelling’ in this way
@issac1071
4 жыл бұрын
Thank you Andy F
@kenonkenkay9426
6 жыл бұрын
thank you. your video is very clearly to understand, I'm sure it will help me pass my mid-term exam tomorrow. lmao
@ValoriYT
5 жыл бұрын
How'd it go?
@spoonyabyss8814
4 жыл бұрын
Ya dude how’d it go
@ameen5586
4 жыл бұрын
Bruh
@Jorge-125
3 жыл бұрын
2 years later. So how was your graduation?
@Ndiedddd
2 жыл бұрын
@@Jorge-125 3 yrs* 😂
@madisonroberts258
Жыл бұрын
Im gonna do great on my test tomorrow
@konvictz0007
6 жыл бұрын
Hi Sal, love your videos. Just need to update it to 1080p, will look sharper on bigger screens.
@braden6973
5 жыл бұрын
Watching this on a 27-inch 4k monitor, Never once noticed the quality. The only thing that matters is the content of the video.
@becca5501
4 жыл бұрын
dang, he did such a great job.
@anushreesolanki4782
4 ай бұрын
If x =at^2 and y=2at, then find d^2y/dx^2. help me with this concept
@amitai8204
11 ай бұрын
very understandable! thank you!
@l.m4631
4 жыл бұрын
thank you so much
@egregiouslytalented2381
Жыл бұрын
Love this
@6-b-46bsricharan2
2 жыл бұрын
That's amazing.
@jimshtepa5423
3 ай бұрын
how does one tell composition of functions from single function?
@beegking
3 жыл бұрын
this is so clear
@enternamehere6686
11 ай бұрын
Would you mind not taking too long to get to the point please
@ernstboyd8745
27 күн бұрын
I think the chain rule is easy to explain as a 2 stage amplifier. so (g{f(x))' = f' * g'
@bayesian2007
5 ай бұрын
Perfect explanation.
@faythe03
5 жыл бұрын
thank you!
@rafsanaakterjannat8066
6 жыл бұрын
great work I don't know that about this
@sameerpokhrel4379
4 жыл бұрын
When we take the derivative of the function f(x), we write the derivative as dy/dx but Sal wrote the derivative of h(x) as dh/dx . So ain't we supposed to write the derivative of f(x) as df/dx? Please clear my doubt.
@Andrew-ok9gt
4 жыл бұрын
It doesn't matter because f(x) and y are the same thing.
@jamessamuel1255
4 жыл бұрын
Can write it as either
@jamessamuel1255
4 жыл бұрын
h(x) can have the derivative h’(x) or dh/dx
@No_BS_policy
2 жыл бұрын
y=f(x) ->>> y is a function of x dy/dx ->>> derivative of y with respect to x, same as derivative of f(x) with respect to x or df/dx
@mohommedameenahmed2099
3 ай бұрын
Nice
@rosskious7084
4 жыл бұрын
Master explanation !
@littlejoestar4
Жыл бұрын
definitely more confused now 😭
@GhoshA
6 жыл бұрын
Voice and presentation is good .
@kennyelliott9164
2 жыл бұрын
Wouldn’t cos x actually be -cos x because the derivative of sin is -cosx
@yaredt4345
2 жыл бұрын
What is happening here, the math is flowing into me 😁😁😁 this is witchcraft man 👏👏👏👏
@freakinbeast
3 жыл бұрын
I was stuck in the same question and he that that question only.
@davidsweeney111
6 жыл бұрын
You do tend to present calculus in a mechanical way and so all the meaning and understanding is missing...
@GhoshA
6 жыл бұрын
David , hmm
@ethanp4050
6 жыл бұрын
stfu
@snickerdoooodle
6 жыл бұрын
"Mechanical way"? What?
@stinkymans5002
6 жыл бұрын
I actually agree with this. I get very lost in the “derivative x” “du dx” “x x x” He doesn’t give any of it meaning
@hawkmoths
5 жыл бұрын
well that's also likely because this is an intro to the chain rule. he is using terms that he likely already explained in a different video.
@ranaAmeer9349
5 жыл бұрын
Shouldn’t we just use the power rule to get 2 sin(x) and that’s it?!!!
@jamessamuel1255
4 жыл бұрын
Rola Ahmed yeah I’m confused where the cosx comes in and why
@sophialaird6388
4 жыл бұрын
Cos x is the derivative of sin x. It’s weird, but yeah
@kshjnbvsmd
3 жыл бұрын
@@jamessamuel1255 have you got any idea now, im stuck in the same confusion..
@what5493
3 жыл бұрын
@@kshjnbvsmd d(f(h))/dx = 2nd line of 4:10 it’s kind of law. If you differentiate it. You want to differentiate of d(f(h)). Firstly if f(h)= (sinx)^2. That means it’s differentiation will be(d/dx (x^n) *d/dx (x). put here x=sinx.
@mattboatman5769
2 жыл бұрын
Yeah, this is confusing me as well. I get that the derivative of sin x is cos x, but where did the second sin x come from in the first place?
@tylergust8881
2 жыл бұрын
It both makes sense and it doesn't make sense... But to be fair I'm still in trig... I don't know too much about the derivatives...
@dazzdazzle8758
3 жыл бұрын
I wish he had used a simpler function instead of sin x
@alep.2672
3 жыл бұрын
I think this one needs a re-do by the same person
@ethencubberly5073
3 жыл бұрын
respect
@kaylam.6264
2 жыл бұрын
So I'm still confused as to what the answer is 🤔
@oddwork2183
6 жыл бұрын
Great
@GEORGINA-topic
5 ай бұрын
What did u say?
@wasimakram-rs5db
6 жыл бұрын
differential geometry a first course by d somasundran PDF mein knsi website sy mily GI???
@dhruvsingh9243
5 жыл бұрын
2:24 the differentiation of sin X will be cos X
@janardhansharma9451
5 жыл бұрын
It will be 2sin x as we are finding derivative w.r.t sin x
@mysteryspy7
3 жыл бұрын
why he multiplied with cos x with 2sin x ................ i am stuck up can anyone please help me!
@PenandPaperScience
3 жыл бұрын
I just uploaded a video where I solve such exercises step-by-step, explaining everything I do along the way. It might help shed some light :)
@mysteryspy7
3 жыл бұрын
@@PenandPaperScience 👍
@xobk
3 жыл бұрын
I recommend a new intro to this intro.
@RemotHuman
24 күн бұрын
2:25 isn't it the derivative of the whole function with respect to the inner function sin(x) or are you saying that d/d(sin x) (x^2) = 2 sin x I think it should be d/d(sin x) (sin x)^2 = 2 sin x
@mattboatman5769
2 жыл бұрын
Where does the second "derivative of sin x" come from at 3:06? I thought we had already established that the derivative of (sinx)^2 is 2sinx.
@flying_asparagus1279
2 жыл бұрын
It's multiplying the outer function times the inner function. If we see sin x as u, then the original function is u^2. So Sal took the derivative of u^2 and got 2u, which is 2sin x. Then he took the derivative of the inner function, sin x, and got cos x. Therefore, the derivative is 2 sin x cos x.
@No_BS_policy
2 жыл бұрын
Nah mate, 2sinx is just dh/dsinx. We are interested to know dh/dx which is equal to dh/dsinx * dsinx/dx. Hence, the chain rule is applied.
@doooofus
Жыл бұрын
@@flying_asparagus1279 what i find confusing is why we multiply the differential of the outer function with respect to the inner function, by the differential of the inner function with respect to x. i must have learned chain rule years ago now, but coming back to it i realise ive only memorised how to apply it sort of mechanically and dont have an intuitive understanding in my head of why it works that way. Sal doesnt really explain that in the video but just gives us the easy way out of thinking about it in terms of the leibniz notation with the fractions, but even points out that this isnt mathematically rigorous.
@adityamukherjee9462
6 жыл бұрын
I feel like I have already seen this video before tho.
@sameerpokhrel4379
4 жыл бұрын
Dejavu!!
@bhubneshwarprasad9554
4 жыл бұрын
Aumsum time
@JJPMaster
4 жыл бұрын
use the chen lu
@abrueck2518
6 жыл бұрын
First comment
@anamikasarkar8862
2 жыл бұрын
You should have used different colour pen
@fantastic_jarod2391
5 ай бұрын
Yeah lowkey that explanation kinda sucked first L khan academy vid ive seen
@ahmetkarakartal9563
4 жыл бұрын
2:16 did you make a mistake? the answer should be sin2x, isn't it?
@chawza8402
4 жыл бұрын
I think he is correct. if you see the upper example. you can replace the Sin x with the a, which is the same x but different x value. the first x is a, and the second x is Sin X.
@jeremychamberlain6332
4 жыл бұрын
You are both correct. By the double angle identity, sin(2x) is the same as his answer of 2(sinx)(cosx)
@brugamer6031
6 жыл бұрын
Btw this video doesn’t not help me because its very different with my school work as i know chain rule is UV-UV % V square
@zalida100
6 жыл бұрын
That may be a quotient rule you are confusing it with - Sal was explaining the chain rule.
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