Continuity and Differentiability

[@TheOrganicChemistryTutor]

Final Exams and Video Playlists: www.video-tutor.net/ Full-Length Videos & Worksheets: www.patreon.com/MathScienceTutor/collections Next Video: kzbin.info/www/bejne/fH2knmp-ptJga5o

[@anirudhvenkatesan2230]

"Differentiability is the continuity of the first derivative" - One of the best quotes in mathematics. Thank you for everything you do

[@puspamadak]

"Differentiability is the continuity of the first derivative"--- this little thing has bugged me for months. Thanks for your efforts.

[@ian.ambrose]

Sorry, that's not correct. If f'(a) is continuous then f(a) is "Continuously differentiable", not just "Differentiable". It's a concept in Real Analysis.

[@tayyaba4632]

@@ian.ambrose but every differentiable function is continuos as well

[@shahadmerani3116]

exactly oh my god

[@harshvardhansingh9682]

Even teachers are not stating this simple thing...😅

[@mohammedanees1113]

I still don't understand crystal clear. What's first derivative function?maybe i dont understand differentiation yet? My mind's confused

[@malthehansen7915]

4AM rn. Exam tomorrow and I'm behind again... Redbull in hand, with caffeine shakes inbound, I want to genuinely say thank you for doing what you do. If I had cash of my own to spend, you'd be receiving a donation and a lengthy email.

[@VahidNesro]

no need for money on the lengthy email bro lol

[@wh0643]

@@VahidNesro a) he’s not talking to you and b) he’s just being thankful bro

[@FA-xh5zg]

im literally in the exact same situation as you .. rip

[@sarahisoto7200]

Literally. I feel like my tuition should go to him lol

[@SandyMandy-xz4ph]

Caffeine at night bad vroo

[@Ghaidaa]

"Differentiability is the continuity of the first derivative" -- الله يفتح عليك ياشيخ

[@zlader-x8084]

رايق

[@lingeshwaranramamoorthy626]

salute to the man who makes this concept look like addition and subtraction

[@destineecassie7143]

I’m from Colorado and my teacher gave me a really cool trick to understand differentiability and continuity. He said “just because you’re in Colorado doesn’t mean you’re in Denver BUT if you are in Denver you HAVE to be in Colorado.” It’s the same thing with continuity. Just because you are continuous does NOT mean you are differentiable but if you are differentiable you HAVE to be continuous. ☺️ hope this helps someone cuz it fs helped me

[@DangQuocNhut]

The title is about one topic, but he always covers many topics in his video. Therefore, I can learn more than one. Love it.

[@en2336]

Your videos are always so lengthy and thorough. I know I can count on them. Your hard work is very appreciated!

[@lonevoyager6026]

yo do u know if a function is differentiable at its endpoints?

[@ts37924]

Yes I think the derivative (slope) of a function exist s at it's end points.. as long as the function is defined at the end point and even it's limit exists and approaches a definate finite value, which at the end points of most functions does.

[@omogboladefalokun]

​@@ts37924But the endpoint of a function would lack a limit from the right, hence wouldn't be continuous? Or am I wrong?

[@ts37924]

@@omogboladefalokun hmm I'm not sure but you do have a point. It may be that the domain of the function doesn't exist on the right i.e the domain (x values) has ended so therefore the function of x ends there to so maybe it doesn't require a limit from the right. But I am no expert

[@tasinferdaousgalib8653]

5 am rn. Exam at 9. Why does it seem so easy all of a sudden? Just thanks a lot man. May Allah bless you.

[@ian.ambrose]

Allah is a murder and a rapist.

[@Edigor100]

Your videos are great because you're doing things differently than other youtubers. Other youtubers only show very trivial examples so there's not much to learn from. You however show problems that are difficult enough that you can transfer the knowledge to harder problems and that really helps me a lot with my understanding about the topics you teach/explain

[@bartroger7734]

Bro what ur doin is legit man ur such a life saver keep up the good work I really truly honestly appreciate it thks 💙

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Yeah he’s awesome

[@keerthanasatheesh9639]

Yeah he's awesome

[@bromaro]

Yeah he's awesome

[@crediblejumper]

Yeah he's awesome

[@nighthawk2566]

Yeah he’s awesome

[@Ychae02]

I studied in class for months : 0 knowledge Watching this video for 32 minutes and 47 seconds : 99.999% of knowledge in my 🧠 Thank you so much.

[@iqrakhanamansari8670]

Hey is this taught in 12th grade in usa??

[@Ychae02]

@@iqrakhanamansari8670 I'm Thai and I needed to study this topic in 12th grade

[@sandippaul468]

plot twist : the 0.001% is the most vital.

[@Sfyn0z]

@@sandippaul468 0.001% is what comes in the exam lol

[@shahadmerani3116]

IVE BEEN STUGGLING WITH THIS FOR MONTHS😭 my college entrance exams are in like 2 days YOU LITERALLY SAVED MY LIFE, THANK YOU.

[@shahadmerani3116]

here again after 6 months bc i didn’t pass :)

[@verifiedgentlemanbug]

@@shahadmerani3116 ayoo what program are u taking in college bro

[@shahadmerani3116]

@@verifiedgentlemanbug um i graduated high school last year but failed my college entrance exams. and in my country everyone basically does the same exams, 7 subjects and based on your score you see what major you can pick-

[@shahadmerani3116]

@@verifiedgentlemanbug and to answer your question properly i have no idea

[@nutella2671]

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[@Vijay_helo]

Bro... I think you are a legend. No one single channel has covered all maths and science for all ages!

[@DadsCornerLew]

Honestly I've spent hours on other sites trying to understand stuff that you explain clearly in just a few minutes. I've never had any real motivation to join patreon but to show my support for what you do I'm about to sign up.

[@manzidelick2752]

I am deeply moved by how differentiability and continuity have been simplified in just 30 minutes, I'm very thankful bro, all my classmates will be impressed and greatly helped by this video 🤝🤝🤝🤝

[@tasongenowoa3758]

If I could have access to videos like this during my university days I would have had a better GPA. You are awesome.

[@AnasKhan-gt5qe]

OH MY GOD you have no idea how much helping are your videos, you are saving grades in the last hours of their finalisation.

[@backflipinspace]

i've never understood continuity and differentiability this well. thanks a lot!

[@shaamjamsi9964]

better and better!! you are the best one of the teacher that i have seen on a youtube !! continue what you are doing is so right!! thank you!

[@هدىسعيد-ق7ق]

THIS IS THE BESTTT CHANNEL EVER TBH YOU JUST A LIFE SAVIER CANT EVEN THINK ABOUT HOW MANY TIMES YOU SAVED MY POOR MATH UNDERSTANDING THANK UUUU 😭👏🏼👏🏼

[@khimannegabuco509]

THIS IS MY FAVORITE YT CHANNEL I LOV U SO MUCH

[@detaqwer]

Thanks man you explanation is easier than some top professors in the country

[@jcmick8430]

The best teachers prob go for better jobs than teaching and arrogant douches become tenured profs 😅

[@SivaSiva-k5t]

Hope these videos would be available for some centuries ... All is well... 🎉🎉🎉 ❤

[@ersinerdem7285]

The goal is to find the rate of change at one point in a function, which is the slope of the tangent line at that point, namely the first derivative. In order to find this, the function should be differentiable at that point. And in order for it to be differentiable, it needs to be continuous at that point. Very well described, thank you.

[@bikashtalukdar9521]

Wahhh bro👌

[@lioncaptive]

You've got it...one must be able to listen carefully and develop a logical comprehension to restate the key points in words.

[@MohitBaboria]

|x| is continuous and x=0 but not differentiable

[@АйданаМейрамова-з7ь]

God bless you. You saved so many nerves of students, keep it up! It's truly appreciated.

[@lesenq.9903]

Can't image the world without this guy, saved me everytime before the exam

[@jaymsf4503]

You explain it better than my textbook for sure. Thank you.

[@lemmesoloher]

this dude right here has been my hero since high school till college

[@humour4kiraanti307]

I from india and i tell you you are the best teacher in the whole fkn world.

[@georgesadler7830]

Professor Organic Chemistry Tutor, thank you for an outstanding explanation and analysis of Continuity and Differentiability in Calculus One. Continuity and Differentiability are important topics in Calculus. This is an error free video/lecture on KZbin.

[@sugarycashew3035]

My first month of calculus made less sense than the first 10 minutes of this video. You are amazing

[@otd119]

Got a test tomorrow and you've literally saved my life.... Thumbs up 👍👍👍👍👍

[@lennyzelfine7850]

Thanks!

[@zakerhussainnazari4064]

well done and thank you , you are a blessing to all people watching your videos.

[@annas7853]

Your voice and speech rate are both really pleasant and easy to focus on.

[@Pandora01-d9d]

Bros name must be in my diploma

[@xyz-fq8lv]

A very nice, clear, and logical explanation!

[@UmarAli-qp6pl]

your method of teaching is just amazing because you explain very deeply. keep up the good work.👍👍👍

[@madhusudhanuppala7530]

Extraordinary skills in explaining the concept 🙏🙏🙏🙏🙏

[@mint7325]

May Allah bless you!!! JazakAllah Khair!

[@Mr.G626]

hahahaha

[@paulscherz22]

@@Mr.G626 fr LMAO

[@navjotsingh2251]

Humzah Khalid calm down lol, it’s the internet, telling people to stop being disrespectful has literally zero effect. Just ignore it.

[@ian.ambrose]

Allah kills millions of people.

[@ian.ambrose]

Allah rapes millions of people.

[@aman45742]

Concept in it's purest form , well explained

[@CrimsonBlade39]

2:27 is wrong, as x approaches two from the left side why approaches negative infinity. You got it reverse with negative 1/x. Good video by the way. Its the small mistakes that need fixing.

[@vaibhavambrale6805]

So grateful for your contribution such a wonderful lecture and deeply understanding the fundamentals

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u are helping me so much this semester bro in almost every course

[@lalitchaudhary6269]

Organic Chemistry Tutor teaching math. Good explanation 👍

[@BalanceWithDani]

This video is excellent!! THE BEST MATH CHANNEL.

[@GobbyRocks]

You are my favorite math tutor! Thank you.

[@minkymoo5773]

Isn't the graph he's showing at 2:33 flipped? The graph he drew looks like the graph of -1/sqrt(x -2) to me, not the graph of 1/sqrt(x-2).

[@RUFAROCHIGORA]

Your videos are the best, you are hard working

[@ManviFunde-cx9vr]

Thank you so much dude like hats off to this man who always saves me from the test the other days like he always solves my minor doubts that are always bugging my head every now and then I appreciate your work so much mannn

[@katlegomaharela]

making it more easier and simpler ,thank you bro

[@ahmedmstafa1]

Thank u so much , 32 minutes of precious teaching 💙

[@kristofdilimombabihosea]

The way I enjoy your videos neh, you won't understand... Keep it up Bro, you changed my study

[@ncedwards1234]

One correction: If f(x) is differentiable, it does NOT mean that f'(x) is continuous (i missed that exact problem before). The differentiability just implies that f'(x) exists at every X value , it could have a jump discontinuity.

[@ian.ambrose]

Thank you. Finally someone who gets it. If f'(a) is continuous then f(a) is "continuously differentiable", not just "differentiable", it's a concept in Real Analysis.

[@ts37924]

​@@ian.ambroseright...I guess the chemistry tutor ment that if f(x) is differentiable at all points then the function f(x) it self is continuous.

[@ts37924]

When you say that f'(x) may not be continuous do you mean that if we were to plot a graph of f'(x) with respect to x then that graph may have discontinuities?

[@googleuser7590]

I did the same in my exam, will i get marks for it?

[@Rishibharti1995]

I am lucky to get your videos , your representation realy wow!👌

[@nakshatraroyrudra716]

Bro, you just save me during the exam, thanks a lot🥰

[@thems2002]

Wow ,i love your videos ,your explanation is amazing.Thankyou So much .❤❤❤

[@hanselito2416]

Not so bad. Two functions joined together. See if they join in the same place or a jump. I hope that's right. Great teaching style.

[@SciTechOddysey]

The way professors make this seem difficult is a skill

[@jannatulmawah7821]

that was so helpful and easy to learn!😍😇

[@chiakikajitani3805]

thank you so much, your explanation is really easy to understand and it encourage me to study

[@ayansuleymanova03]

I don't know how I can send my all thanks to you. may God save you!!!

[@stephankubicki2473]

Unfortunately this video contains some serious errors. Differentiability at a point is NOT defined in terms of continuity of the first derivative, nor does it even imply that the derivative is continuous at that point. The standard example is the function defined by f(x) = x^2 * sin(1/x) when x ≠ 0 and f(x) = 0 when x = 0. This function is differentiable for all real numbers x, but the derivative f'(x) is NOT continuous at x = 0. Differentiability at a point simply requires that the derivative exists at that point (ie. the limit of the difference quotient, as h -> 0, exists). It can be shown, however, that differentiability at a point implies that the derivative does not have a "jump" discontinuity at that point. This is because derivatives must satisfy the intermediate-value theorem. But this is a significant, non-trivial result, typically requiring the mean-value theorem for its proof.

[@ian.ambrose]

True. HE FOOLED ME FOR MONTHS! Thank you for talking about this! There's a concept in Real Analysis called Continuous Differentiability which states that f'(a) is continuous then f(a) is continuously differentiable. Am I right, sir?

[@didiruhyadi4798]

I'd learned over night and still didn't understand, until I see this video. Thank a lot brother

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You are a true hero. You're an inspiration.

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Your videos save my life every day in maths

[@skylalesalaise4464]

He draws the best graphs.

[@phani2820]

Man ur a beast with ur concepts

[@bahha6303]

thank you this saves me a B on ap calc.

[@shamineywalsh-dupuis6520]

Thank you so much for that detailed explanation. It really helped me to grasp these two terms and understand their relationship.

[@christianneee]

I appreciate this channel🥰❤️

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I really appreciate 🙏 this tutorial is really helpful #stayblessed

[@omarmagdi2732]

the prophet of science on internet

[@mohammadismailhossain6435]

Differentiability describes the continuity of the first derivative. 👌

[@phuzo3320]

Thanks for building my concepts

[@ILIOS_1]

@ 24:27 Where does the 0 come from? Fast Forward to the second function, and you plug 3 into the x, where did you get these numbers from, I am confused on where the numbers originated from

[@JoaoMane_IPSLEI]

Remember the derivative was 3x^2, and the point of transition in the piecewise function was x=1. Therefore if you plug x = 1 into the derivative it's 3 * 1^2, which is 3. Hope this helps.

[@ILIOS_1]

@@JoaoMane_IPSLEI one month later... thank you

[@Tenems1]

you are a total life saver. Thank you so much !!

[@bhilaksh6923]

very nice explaintion ❤❤

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الف الف و ارجعلك تاني ، ربنا يباركلك

[@suncult]

The video is very useful. Thanks for helping.

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Thank you so much Finally I understand 😩😩😄😄

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Gorgeously explained thank you

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I love your videos. thank you so much from a very much older student that's gone back to school

[@Rishibharti1995]

I like more graphical approach and step wise prossiding

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Thanks again, the explanation was useful to me again

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omg i love your voice so much

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[@vidhishukla3033]

Thanks brother, it was very helpful.

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Wow😇👏👏👏 Thank you

[@jimmyonis]

HONESTLY SIR U A THE BEST TO ME. WELDONE

[@themasculinetransformation]

Honestly I understood alot but not all because I don't study this with English i study it with french because I'm in north Africa 🥲 I wish i study it with English I don't understand french at all and I'm forced to study math science computer science and technology With french in highschool because you know AFRICA .... I wish i study with English or Arabic Thanks alot my friend

[@fatmaraouf4419]

Thank you I finally undrestand👌👌

[@daisynwobodo7340]

I need to get an A in this course

[@anmoldedha4089]

in 2:30 he explained a infinity discontinued function example 1/x-2 and plot it in graph as well is he plot the graph wrong ?

[@zihanzhao2153]

超级超级超级感谢老师我会了 考试全靠您