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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.
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.
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 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
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
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 🤝🤝🤝🤝
@@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-
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.
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
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.
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 RUclips.
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.
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.
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?
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
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.
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.
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?
I Have a Question (more like confirming),.......so, there are situation where c can be continuous but not differentiate, Then the only Situation I can Guess for Differentiable is to be true is ALWAYS a straight line(a Linear Function), .........or do we have another example
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
Hi I have a question for the dx/d of x^1/3 can you say it is not differentiable at 0 because the domain x cannot be equal to 0? Is differentiability and domain related?
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"Differentiability is the continuity of the first derivative"--- this little thing has bugged me for months. Thanks for your efforts.
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.
@@ian.ambrose but every differentiable function is continuos as well
exactly oh my god
Even teachers are not stating this simple thing...😅
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.
no need for money on the lengthy email bro lol
@@VahidNesro a) he’s not talking to you and b) he’s just being thankful bro
im literally in the exact same situation as you .. rip
Literally. I feel like my tuition should go to him lol
Caffeine at night bad vroo
"Differentiability is the continuity of the first derivative" -- الله يفتح عليك ياشيخ
رايق
salute to the man who makes this concept look like addition and subtraction
"Differentiability is the continuity of the first derivative" - One of the best quotes in mathematics. Thank you for everything you do
The title is about one topic, but he always covers many topics in his video. Therefore, I can learn more than one. Love it.
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.
Hey is this taught in 12th grade in usa??
@@iqrakhanamansari8670 I'm Thai and I needed to study this topic in 12th grade
plot twist : the 0.001% is the most vital.
@@sandippaul468
0.001% is what comes in the exam lol
Your videos are always so lengthy and thorough. I know I can count on them. Your hard work is very appreciated!
yo do u know if a function is differentiable at its endpoints?
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.
@@ts37924But the endpoint of a function would lack a limit from the right, hence wouldn't be continuous? Or am I wrong?
@@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
Bro what ur doin is legit man ur such a life saver keep up the good work I really truly honestly appreciate it thks 💙
Yeah he’s awesome
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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
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 🤝🤝🤝🤝
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.
Allah is a murder and a rapist.
IVE BEEN STUGGLING WITH THIS FOR MONTHS😭 my college entrance exams are in like 2 days YOU LITERALLY SAVED MY LIFE, THANK YOU.
here again after 6 months bc i didn’t pass :)
@@shahadmerani3116 ayoo what program are u taking in college bro
@@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-
@@verifiedgentlemanbug and to answer your question properly i have no idea
@@shahadmerani3116 you should be ethiopian ryt
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.
If I could have access to videos like this during my university days I would have had a better GPA. You are awesome.
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i've never understood continuity and differentiability this well. thanks a lot!
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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
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.
Wahhh bro👌
You've got it...one must be able to listen carefully and develop a logical comprehension to restate the key points in words.
|x| is continuous and x=0 but not differentiable
God bless you. You saved so many nerves of students, keep it up! It's truly appreciated.
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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 RUclips.
So grateful for your contribution such a wonderful lecture and deeply understanding the fundamentals
Thanks man you explanation is easier than some top professors in the country
The best teachers prob go for better jobs than teaching and arrogant douches become tenured profs 😅
You explain it better than my textbook for sure. Thank you.
Hope these videos would be available for some centuries ...
All is well...
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A very nice, clear, and logical explanation!
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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.
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Organic Chemistry Tutor teaching math.
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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.
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.
@@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.
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?
I did the same in my exam, will i get marks for it?
You are my favorite math tutor! Thank you.
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
making it more easier and simpler ,thank you bro
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.
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.
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?
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Thank you so much for that detailed explanation. It really helped me to grasp these two terms and understand their relationship.
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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).
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I Have a Question (more like confirming),.......so, there are situation where c can be continuous but not differentiate, Then the only Situation I can Guess for Differentiable is to be true is ALWAYS a straight line(a Linear Function), .........or do we have another example
very nice explaintion ❤❤
I appreciate this channel🥰❤️
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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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Differentiability describes the continuity of the first derivative. 👌
best video ever
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By the last example, does it mean you can have a derivative without the function being differentiable?
Could someone please say the name of this theorem or corollary that " the function is differentiable if its first derivative is continuos"? Please🙏
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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
Hi I have a question for the dx/d of x^1/3 can you say it is not differentiable at 0 because the domain x cannot be equal to 0? Is differentiability and domain related?
Oh nvm I didn’t see that you answered this at the end
Thanks dear ❤️❤️❤️