Visual Derivative Definition!

[@ОравськийДушан-д3п]

The best explanation! I like how you explained the reason why we use limits. I wish I saw this video earlier

[@MoguMogu818]

Back when these videos to me were gibberish now make me realize how much easier I would've had it if I had studied calculus by trying to understand the math instead of trying to force myself to do the math problems.

[@SaiManognyaDesetty-bs3gp]

I properly understood what a derivative is after two years of learning calculus. Same goes for why limits are necessary. Thank you very much for this short and highly informative video!

[@1optimus_princeps1]

You showed me the logic in 30 seconds of the formula that was shown when I was in high school and that I have known by heart for two years. I am both very grateful to you and angry at the education system.

[@Blackwidow795]

Single short made me subscribed to you... Your explaination is great 🙏🏻 Love from India

[@MathVisualProofs]

Thanks! Welcome!

[@supermarioenthusiast5881]

Beautiful visuals man! Is there also a possibility for you to do this demonstration but with x->a replaced with the h->0 where h represents height proof for derivatives?

[@MathVisualProofs]

Tried to do that here but ran out of time :). I’ll see if I can do a Follow up

[@DeanCalhoun]

simply take this formula and substitute a with x+h. you will get the familiar formula, and if x is approaching x+h, then h must be approaching 0

[@prajwalbhoite9865]

Beautifully explained, thanks

[@liammoore1066]

This video is a really clean explanation

[@hakeemdj368]

👍 👍 👍 👍 👍 👍 👍 👍 👍 👍 👍 🙏 the best explaination

[@LambdaGroup]

This is the best explanation I’ve seen yet. I’m planning on taking calculus next year, so this helps a lot!

[@rb_gamer007]

Best explanation

[@edwardgongsky8540]

Please do partial derivatives and chain rule! Your vids are awesome.

[@MathVisualProofs]

Partial derivatives might be on the way! :) Thank you for this comment!

[@andycheng4372]

講解得非常清楚，謝謝老師🙏

[@godlikegaming1363]

Excellent 🎉

[@michaelmaged2875]

You finally gave me closure as I now finally understand what I've been cramming in 11th grade and never understood till just now!! ❤❤

[@vladimirrodriguez6382]

Magnificent graphic explanation 👏👍😊

[@MathVisualProofs]

Glad you liked it!

[@shuvra4352]

Best explanation...

[@greywolf7422]

It was good during the first 20 seconds, but such an explanation needed at least 2-3 minutes to let the various variables in the presentation settle with the audience. Good in theory maybe if it was done in a regular video format or linked to in the shorts description as a full video. Not all students who come across such explanations will be able to follow such a rapid pace explanation, especially the last 20-30 seconds.

[@treybell40501]

I wish I could love this video bc you don’t know how much this changed my perspective

[@jarige4489]

I simply love your channel, it reminds me why math is beautiful!

[@MathVisualProofs]

Thanks!

[@Froze-rt2bk]

@@MathVisualProofscan u explain to me what the power rule is

[@omagoss]

Thank you very much

[@Inspirator_AG112]

*Step 1:* Construct a tangent line at (a, f(a)). *Step 2:* Construct a right triangle whose base is 1, and whose hypotenuse is on the tangent line. (Ideally at (a, f(a)).) *Step 3:* Measure the height of that right triangle; that should be f'(a).

[@MathVisualProofs]

How do you construct the tangent line?

[@Inspirator_AG112]

@@MathVisualProofs: I was mainly talking about if the curve was a physical object or drawn on paper.

[@tomedgar57]

@@Inspirator_AG112 :) that works

[@TinyFoxTom]

Is any side of the triangle colinear with either axis?

[@robot652]

thanks bro

[@annahlee]

this youtube short was amazing for review. Thank you!

[@barsbasaran8904]

such a clear explanation ! nice work

[@TheSerpion148]

Very good❤

[@rishabhnarula1999]

Nice, I had posted a video on my channel about a simple visual proof of the fundamental theorem of calculus, you could make a nice short like this on that.

[@ndrcrypto]

amazing

[@anandtewani7591]

Where the hell was this creator when I was needed the most 😢 Btw I completed my school 14 years ago. Anyways I wished I would have got the exposure to such informative videos earlier...life would have been definitely different today.

[@GabriTell]

It's never late to change ✨️

[@jackkalver4644]

Fun fact: If you hold the point at x=a and zoom in, the portion of the graph you can see will look like the tangent line at x=a.

[@あかし中村]

OMG👁️👄👁️ What a explanation

[@pawanyadav3399]

Nice explanation🙏🙏🙏🙏 sir

[@MathVisualProofs]

👍😀

[@rawvoxel]

I can't tell you how many videos I watched on this topic that were like 10 minutes long and confusing as hell, and this tiny video made it make sense.

[@qenrl8474]

Your explanation make it so easy to understand! Literally only have introductory knowledge and limits and you still managed to do it. Only thing im confused about is why would you need to find the instantaneous rate of change?

[@MathVisualProofs]

It’s nice to know how fast a process is changing at any instant. Then you kind of know what to expect. You can study rates of rates of change and then get a better picture. For instance you can tell if emissions are increasing or decreasing and if they are decreasing at a decreasing rate. All of this can be done analytically once you have a model of the process.

[@Ben-u8w]

Thank you so much it really helped a lot😊

[@Froze-rt2bk]

I'm just a 6th grader but ty for explaining this to me now I'mma start taking notes on calculus to impress my friends

[@Froze-rt2bk]

I have been studying this for one day now I actually have a strong understanding of it I also now how to find derivatives and antiderivateives also know how to do limits

[@vigneshbalaji21]

Nice explanation. Derivative is based on secant line

[@sweetNsalty-T]

TYSM

[@TOUKAYSWISSI]

Good!

[@MathVisualProofs]

Thanks!

[@wyboo2019]

this is great for functions between one-dimensional vector spaces, but i prefer the interpretation of "how a small movement in the input spaces changes the output space" interpretation to generalize to multi-dimensional spaces

[@Beegeezy144]

Beautiful.

[@helldestroyer]

Thanks for nice video ❤❤

[@ceebad8985]

Can you do something similar but for the fundamental theorem of calculus? Thank you, your videos have helped me a lot ❤️.

[@sraidimohamed5367]

I love you man

[@Mmmmgh34]

Just WOW

[@hugoviloriagonzales2331]

Difícil para mi ha sido comprender antes, pero con estos simples videos, me aparece la Claridad.

[@greywolf7422]

It was good during the first 20 seconds, but such an explanation needed at least 2-3 minutes to let the various variables in the presentation settle with the audience. Good in theory maybe if it was done in a regular video format or linked to in the shorts description as a full video. Not all students who come across such explanations will be able to follow such a rapid pace explanation, especially the last 20-30 seconds.

[@dominicellis1867]

And you can use the angle differential to bypass computing total differentials by simply taking the anti tan of dy/dx.

[@Kryy213]

hey! i love this explanation, it's clear and concise! could you do the same for the second derivative ?

[@MathVisualProofs]

Hmm... the second derivative is just the derivative of the derivative function... so it is just this again but applied to the derivative. Or do you mean something else?

[@1234i-o8q]

It's Lagrange's Mean Value Theorem

[@AmanKumar-wd6hm]

KZbin without distraction videos 🗿🗿🗿🗿

[@HkRines]

There is no "INSTANT" rate on "CHANGE". That explains why you cant devide by zero. If you take a picture of an car, you can compute cars velocity. Because there is no "INSTANT" change of cars position (Speed)

[@TalSzor]

My HS physics teacher used the same visual idea when he taught us derivatives for the first time.

[@MathVisualProofs]

Glad to hear it!

[@lory3771]

Every Calculus student just groaned at having to do six hundred problems using the formal definition of a derivative

[@jonathanreynolds2625]

Holy fucking cow biscuits! I've been struggling with this exact thing the last few days and I finally get it!

[@MathVisualProofs]

👍😀

[@ms.andrea172]

I learned the Korean alphabet in less than 2 weeks, about the same amount of time for the Japanese alphabet, but this did not compute. Lol

[@Questiala123]

Or just d approaches 0 and delta = d of delta(y)/delta(x).

[@unknown-lg9oh]

Bro cooked my brain and ate it

[@abdeljalilpr2033]

Please the proof of the derivative of the product of two fonctions

[@MathVisualProofs]

I’ll see what I can do.

[@tandomrandom]

Can you share your manim code for each short?

[@elixpo]

Manim at its peak xD

[@yanggang4352]

To me the most interesting thing is any tangent passes through 2 contiguous points and not 1! It's unfortunate that nobody teaches this, but it's true

[@kbin7042]

That's false

[@Drift1]

You explained this in under a minute compared to an hour lecture I ha d

[@antotot04]

please please please please, do this with the limit definition i need it! Thank you for your work, is super helpful

[@Miguel_Noether]

Cantor set: I'm about to destroy this man whole career

[@sumithadavid5841]

So what will be the graph of double differentiation of that curve y=f(x)

[@Lorz]

Nice explanation. Only thing is the wording: "instant rate of change". Its an oxymoron. Instant describes a specific point in time. Change is a timespan so its not the same

[@p07a]

Can you do this but for the epsilon delta concept?

[@MathVisualProofs]

I am sure I can't do a better job than 3blue1brown: kzbin.info/www/bejne/oZepZWODnrhqsKM

[@agoogleuser2507]

now do this but with celebrities and politicians

[@Vighnesh_Graphicdesinger]

3blue1brown Khan Academy Crash course Organic chem tutor None of their videos led me to understand this bt your 60 sec short did I thank you very much 🙏

[@MathVisualProofs]

Glad to hear that

[@MathVisualProofs]

@@nishantkumarsingh5002 I am not.

[@AzureSpike]

Isnt it more aesthetically pleasing to change to (f(a) - f(x))/a-x?

[@Shaeffen_]

You'd be able to make a good video on riehman sums

[@Ryancodehcs]

Sir , this has helped me deepen my understanding of derivatives on an intuitive level but I have query, why would we want to the instantaneous rate of change of cosx is sinx , while this may sound stupid I cannot understand the usage of this outside of scope of displacement graphs (to find speed).

[@maki9462]

Nice

[@beanman7516]

Rolle's theorem lore

[@Cactly]

I haven’t taken calculus yet. This sounds like a different language

[@jujubelaa1339]

How do you make theese animations?

[@musashi4856]

One day we'll develop maths that directly address Zero and Infinity ♾️/0 and finally put clothes on all the emperor's theoretical theories.

[@pureanimations4260]

What is an alarming wave called? A warning sine.

[@kingonion2102]

I know that the derivative at x=a is equal to the slope of the tangent line at x=a, but how can we be sure of it? Isn't it just a very close approximation to say that the derivative is the slope of the tangent?

[@lenin1206]

What does he mean by instante rate of change?

[@danangwiratama6887]

What apk do you edit math animation like that?

[@MathVisualProofs]

I use manim for these animations.

[@koponstanley4]

What about d²y/dx² Is it rate of change twice?

[@kirbofn524]

Isnt the sentence “Instant rate of change” an oxymoron? Change is a difference in time, but if it’s instant, there is no time?

[@beautyreveal1715]

What about the visualization of derivative of sin(x) to cos(x)

[@MathVisualProofs]

It’s on my channel. Wide format has many details. Short shows just the way to think about derivatives.

[@Lashistoriasdelilith]

The rate of change means the velocity?

[@MathVisualProofs]

If you are measuring rate of change of position then yes.

[@mrawesome2704]

Are you on the manim discord channel?

[@MathVisualProofs]

Sometimes but rarely.

[@Dhruv45124]

When we say Derivative of sinx What do we mean Do we mean finding the slope of tangent of whole graph or what, please help as I am new in calculus

[@MathVisualProofs]

This means finding the function that outputs the slope of the tangent line (or instant rate of change of the sine function at the right input) . Check this one : kzbin.infoOD6WBF5lVwA?feature=share

[@Dhruv45124]

​@@MathVisualProofs ok i got that! 😊 I have one doubt left-: How can you have a variable 'x' on x axis if the graph is of y=f(x) Because I have seen that, there exists points other than x on x axis for example, b, c, d etc... And when we put their value we get f(b), f(c) respectively. Also thank you

[@ScarletEmber64]

​@@Dhruv45124 basically, the x-axis represents x itself There doesn't really exists a "point x", x just represents all possible values we can input into our function so when we say that we have f(c) for example, that just means we are setting x to be equal to any arbitrary point, which we call c here, and get the value for f(x) at that point

[@prithvisinghpanwar007]

wait wait instant rate of change???!??? htf can you find it i took a photo of a uniformly moving car in a straight line tell me the acceleration of the car

[@robertsullivan9833]

X to a is the secant line the average for the curve or just between the two points?

[@MathVisualProofs]

Just between two points.

[@abrga.l]

when do people usually start to learn these?

[@louisl2747]

High school if you're in specialised math classes or college/university for most people studying science

[@amitvikramsinghparihar8241]

LMVT

[@mohammadbajoouri568]

It is a+ or a-?

[@Black45-FV]

Hello hello you are explanation is so beautiful but I can't understand English so much😢

[@dranandamay]

So limit is to find 0/0, without dividing 0 by 0 😮

[@GabriTell]

Not quite...

[@Malke864]

0:00

[@decksforgg9883]

I don't understand how is that change. Like it's just the point what's changing

[@scrappy4170]

Great explanation but "instant" and "rate of change" don't make sense next to eachother

[@Boltkiller96]

you came here after watching 3b1b's video right?

[@scrappy4170]

@@Boltkiller96 it's just something in the back of my mind and now when I see people say that, it just annoys me a bit

[@epicchocolate1866]

@@scrappy4170 fine the infinitesimal change variation in y wrt an infinitesimal change in x

[@neitoxotien2258]

My question is why does it say x approaches a, not approaches 0? Am I missing something? If so please enlighten me. Thank you

[@MathVisualProofs]

This is the definition of the derivative at a point. We let x get close to a. You might be thinking about the definition of the derivative function, where we replace a by x and x by x+h. Then we let h go to zero.

[@karthikkumar5822]

Why would teachers complicate this to us??

[@lahiru1k]

OMFG everything clicked!!!!

[@scrumdiddlyumptious979]

Does the limit give the exact value of the slope at that point? It is a bit difficult for me to understand as the limit actually talks about what is happening around that point that than that point itself right? Please help me as I am new to calculus

[@MathVisualProofs]

The limit is the exact value of the tangent line slope (provided it exists)

[@scrumdiddlyumptious979]

@@MathVisualProofs thank you!