No joke, I passed differential calculus in college without knowing this. Our teacher only gave us the formulas without further explanation. This video sure helped a lot to answer a few questions, thanks!
Did you not learn this in highschool? The fundamentals and visualisation happens in school, ofc in college they're just gonna give you formulas to solve problems.
@@all.handles.are_taken I was talking with some friends from my career about this topic and none seem to knew about this. So I guess it must be due to differences in the teaching methods of different countries (I'm from Mexico)
It isn't, a limit just means that for any sequence x_n such that for any given ε>0, there is a number N so for all n>N: |x_n - x| < ε. So it is saying, however close you want me to get, I can pick a number so that it is closer for the rest of the sequence.
That's actually incorrect when you're doing the limit you're actually checking for convergence add a point not when something is infinitely small or close to zero that's actually not what you're looking for you're looking for where the two sides link up together or where they converge because something you should probably know is that limits if the right limit is not equal to the left limit then that limit is invalid so thusly your explanation is just poor
I don't know whether to laugh or to cry at the fact that I fully understand why the formal definition of a derivative f(x+h) - f(x) /h. The entire school year, I just memorized it because I thought it was an arbitrary formula some guy found.
It means that it applies anywhere, since slopes remain constant only for linear polynomial functions. Because in a Quadratic Polynomial function for example, as you get the higher, the rate change increases. Therefore we cannot have a singular value to define the rate of change(slope). Hence we cannot use the secant line. We then use the slope of the tangent line(or a point that only intersects the function at once). As we get the points closer, the distance approaches zero. So if we get the closest to zero we possible can, the distance becomes practically the same across all input values. Hence the limit!
Its crazy how many really fundamental concepts I am just beginning to appreciate from these videos almost a decade after passing calc 3 in college with flying colours. Is there anyone else who didn't know that derivatives are actually limits lol. Please don't stop making these!
I just realized why it’s not some arbitrary point in the middle of the two. The second x value is literally defined as the first + a distance h. If you make that distance infinitesimally small, you get closer and closer to the first x value. So you have to be describing the slope, or instant rate of change, of the first x value.
How sad i used to really love math, being able to learn, to understand and to love all of these thing make me fell something big, like i can see through the whole world, this clip is what i had already study and find out on my own few years ago, but something happen, i stop learning and using math, seeing this clip today remind me how beautiful it is, i still joyful like a child just like the day before, it still beautiful like the day i lost it ❤❤❤
I'm currently studying BSc Computer Science and I cannot delineate how much these videos have actually helped me understand the work on such a fundamental level, thank you so much and please don't stop making these incredible videos❤
Broooooo, this is the best visual representation of derivative that ive seen by far and all of a sudden i understand why the derivative formula is like that now.
This is the exact thing that made me realize I can do math without just memorizing formulas, but actually understanding what they mean. I have a graduate degree in engineering now.
One of the reason the derivative was invented is to determine the velocity (or the acceleration) of a moving object in any known instant not just in a certain period of time, thats why it is dy/dx while dx a positive value very close to 0 means dx tends to be an instant or point according to the dimension of x
Man, there’s a lot of things missing in there. Historically speaking… but boy, does that even matter? As long as knowledge is being shared !! I love this!
This video is so fucking amazing, i dedicated a lot of time trying to figure out how this formula works and this video explained so easily, great job keep it up!
This is how you find the derivative of a function by first principles. Just input your f(x) for f(x) and f(x+h), you replace all the x's in the function as (x+h). To find the derivative
And then you calculate after that you merge by substituting h with 0 giving you the function to find the slope which is in the case of f(x) = x^2 Is 2x
The brainrot got so bad it flip around and turned into braingrow
this is call minus brainrot
@@vahid9749 brainrot minning
Negative brainrot
Limit of brainrot
Minus times minus equals plus
The person who created this is a modern genius
if you count the 17th century modern then sure
It’s crazy how limits somehow paved the way for so many applications of calculus in STEM that literally shape the world
It False derivative idiot it has to bee the tangent in a point of the curve because it an exponnantial Function
This is over 300 years old.
@@absentchronicler9063He’s clearly talking about the integration of derivatives into brainrot style content ya pseudo intellectualism extraordinaire
why am i learning everything through brainrots now...
interesting...
This is not a brain rot
If you learn something
brain nourishment
me i got these math brainrots after watching khan academy for a week or so
more like braingrowth
No joke, I passed differential calculus in college without knowing this. Our teacher only gave us the formulas without further explanation. This video sure helped a lot to answer a few questions, thanks!
Did you not learn this in highschool?
The fundamentals and visualisation happens in school, ofc in college they're just gonna give you formulas to solve problems.
@@all.handles.are_takenNot everyone takes calculus in high school
I learned this in High school
@@all.handles.are_taken I was talking with some friends from my career about this topic and none seem to knew about this. So I guess it must be due to differences in the teaching methods of different countries (I'm from Mexico)
It's nice to know how it works though.
brain enrichment
This is what tik tok should be
It's like putting so much sauce on your vegetables you can't even taste the broccoli anymore
Braingrow
Faaaaccctss
Brilliant..
The explanation
Wonderful and simple explanation.
brainrot ❌
brain nourishment ✅
It’s not really about as close as you can to 0 as humanly possible, it’s as close as you can get to 0 as inhumanly possible
He used the right terminology before, "infinitesimal", I don't know why it wasn't repeated here
It isn't, a limit just means that for any sequence x_n such that for any given ε>0, there is a number N so for all n>N: |x_n - x| < ε. So it is saying, however close you want me to get, I can pick a number so that it is closer for the rest of the sequence.
Finally something useful in comment section😂@@maxcarroll8639
That's actually incorrect when you're doing the limit you're actually checking for convergence add a point not when something is infinitely small or close to zero that's actually not what you're looking for you're looking for where the two sides link up together or where they converge because something you should probably know is that limits if the right limit is not equal to the left limit then that limit is invalid so thusly your explanation is just poor
@@maxcarroll8639based limit def
What an elegant answer, explained through memes.
these aren't memes bro, this is just ai voice of two people, with a video of both of them
I can't believe I ACTUALLY learned something out of this, this is surprisingly well explained
Here I am, procrastinating for my calc final, and then this pops up. 😅
Good luck! If it's done, how did you do?
The universe has its ways😂
I don't know whether to laugh or to cry at the fact that I fully understand why the formal definition of a derivative f(x+h) - f(x) /h. The entire school year, I just memorized it because I thought it was an arbitrary formula some guy found.
That "some guy" is mf Isaac Newton
This is why you need RUclips for math 😭 schools just teach us the bare minimum to be able to take an exam, youtube teaches us how math actually works
You either had a really shit teacher or you didn't pay attention. This should be the first thing explained.
How do you think people make formulas? 💀 they don’t just pull it out of their ass
Bruh people dont pull random shit outta their ass and call it the derivative 💀
I’ve been learning this for nearly two weeks and this video made me understand it better than anything my professor has taught me💀
It means that it applies anywhere, since slopes remain constant only for linear polynomial functions. Because in a Quadratic Polynomial function for example, as you get the higher, the rate change increases. Therefore we cannot have a singular value to define the rate of change(slope). Hence we cannot use the secant line. We then use the slope of the tangent line(or a point that only intersects the function at once). As we get the points closer, the distance approaches zero. So if we get the closest to zero we possible can, the distance becomes practically the same across all input values. Hence the limit!
Differentiation from First Principles doesn’t need to be complicated, when explained like this it’s very easy to understand
This is the smartest thing you will see in yt shorts
Its crazy how many really fundamental concepts I am just beginning to appreciate from these videos almost a decade after passing calc 3 in college with flying colours. Is there anyone else who didn't know that derivatives are actually limits lol. Please don't stop making these!
Limits are a fundamental part of calculus. Are you sure you did multivariable calculus without knowing this?
AI has no limits.
ive watched tons of videos explaining calculus and still struggled until now, thanks man.
I just realized why it’s not some arbitrary point in the middle of the two. The second x value is literally defined as the first + a distance h. If you make that distance infinitesimally small, you get closer and closer to the first x value. So you have to be describing the slope, or instant rate of change, of the first x value.
please continue bro, you're the best, this help me alot
the power rule is my favorite
How sad i used to really love math, being able to learn, to understand and to love all of these thing make me fell something big, like i can see through the whole world, this clip is what i had already study and find out on my own few years ago, but something happen, i stop learning and using math, seeing this clip today remind me how beautiful it is, i still joyful like a child just like the day before, it still beautiful like the day i lost it ❤❤❤
I'm currently studying BSc Computer Science and I cannot delineate how much these videos have actually helped me understand the work on such a fundamental level, thank you so much and please don't stop making these incredible videos❤
3 brown 1 blue look it up might help u
Broooooo, this is the best visual representation of derivative that ive seen by far and all of a sudden i understand why the derivative formula is like that now.
When ( - ) × ( - )= ( + )
Brain rot × Brain rot = Brain revive🎉
Reverse brainrot technique
@@condoriano3533 reverse brain rot jutsu😌
Is actually so fun to understand maths by visualising
Man for the first time, I literally got to know about the exact details of this formula, thank you so much man.
This is the best explanation of derivative by far
My brain aint rotting no more
This is the exact thing that made me realize I can do math without just memorizing formulas, but actually understanding what they mean. I have a graduate degree in engineering now.
no way i learned that in ez way in 1 short like i never thought ill learn it in this fast, respect man. ❤
Pretty good explanation
I love your content bro…wish u could make longer formats
This makes more sense that a whole year of learning A level maths
This is actually understandable
AI gettin too real man
my god if you made them with twenty one pilots band members i’d be passing math with flying colors this channel is so cool
If only it was recommended to me a year ago when i was in 12th grade
oh my god im done with calc for high school and i just realised why thats the formula for derivative 😭🙏
Why is this in my recommended and why did i watch all of it
Bro ghis is the best idea for a channel ever congrtats learning so much
Please never stop making these
They explained it better than my school calc teacher
Thanks, it's above my grade but your explanation made it easy. Keep making content like this man, all my support to you l.❤❤❤
Now I understand what I have been learning
One of the reason the derivative was invented is to determine the velocity (or the acceleration) of a moving object in any known instant not just in a certain period of time, thats why it is dy/dx while dx a positive value very close to 0 means dx tends to be an instant or point according to the dimension of x
That is Leibniz notation, which isn't the original notation.
What you’re doing is awesome, keep it up
This actually taught me something.
ain’t no way brain rot maths
ain't no way, brain rot little kid right here
the visuals helps big really ill sub
Bro you're good.
Damm❤✅
Videos like this make me contnue watching shorts
This was lowkey better than my calc teacher’s explanation, and she’s a good teacher
Thank's for tutorial now I understand everything.
This new RUclips really appeals to me. All these celebs are now in the zone at last!
My brain is rotting and expanding simultaneously
that doesn't make sense mofo
Seriously I wish I found this sooner ❤.
Jeez
I didn't know the definition was so simple
Omg After Wasting 3 Hours And Now That My Brain Wasn't Braining + Plus Headache I've Got It From This 😭 Thankkk Youuuuuuu 🖤
Man, there’s a lot of things missing in there. Historically speaking… but boy, does that even matter? As long as knowledge is being shared !! I love this!
This ain't brain rot, this brain enhance
YOOOOO THANK YOU JAKE PAUL
yikes, its bad how many people weren't aware of this...
The brain rot got so bad it became brain fertilizer 💀
it actually pretty dope that I can learn stuff while being brain dead 😂
YOOOOOOO THE EXPLANATION IS GOOD AF
You need to do this for the hawk tuah podcast
How did I learn all this at school without knowing this
calculus memorisation moment :(
Ladies and Gentlemen, the birth of calculus.
Bro just taught us how to differentiate by first principles 🔥🔥🔥🔥🔥🔥
I really wish I studied a math heavy degree in college now😭
pretty sure this video just explained proof of differentiation from first principles way more clearly and concisely than my a-level maths teacher 👍
i didnt really understand the definition in my class so this is was a very helpful video
I had this test last week, and I aced it! (I think so, at least)
Wtf that was so good
literally the definition
morgan freeman teaches the core of calculus in 40 seconds... I love the internet
This video is so fucking amazing, i dedicated a lot of time trying to figure out how this formula works and this video explained so easily, great job keep it up!
I have already passed calc but this made me look at it differently
This is how you find the derivative of a function by first principles. Just input your f(x) for f(x) and f(x+h), you replace all the x's in the function as (x+h).
To find the derivative
These videos are goated
thanx bro u deserve 1 more subscriber
This is actually a very decent explanation 😂
This is excellent
Jake literally never talks about math a day in his life
More of this needed
And then you calculate after that you merge by substituting h with 0 giving you the function to find the slope which is in the case of f(x) = x^2
Is 2x
teachers never teach like tyhis
btd6 moab health ramping 💀
This is the first principle of differenciation
how i wished they explained the first principle in my school
I prefer using delta x cause its just comfortable for me to use.
Well I mean the explanation where it says “slope at a single point” is technically wrong
You're right guys
Why didn’t my math teachers ever explain it like this
The best teacher ever
To be motivative, derivative is the linearization of a function, and the first principle is just the way to calculate the linearization if it exists.
and this is what are called "differentiable"?
@@ismaelrodriguez9038 differentiability is just determine if a function has unique linearization. If it has, then it is differentiable.
youtube recommends me this after i failed calculus 3 times