Visual Derivative Definition!

This video animates the idea behind the derivative of a function. We show how to think about the definition of the derivative of a function visually by using a limiting process of slopes of secant lines to obtain the slope of the tangent line (which measures the instant rate of change of a function at a point).
#manim #calculus #derivatives #derivative #tangentline #slope #parabola #mathvideo #mathshorts #math #visualmath #graph #linearapproximation #secantline #instantrateofchange #averagerateofchange

[@user-xd5gq8mp5e]

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

[@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

[@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!

[@AmanKumar-wd6hm]

KZbin without distraction videos 🗿🗿🗿🗿

[@annahlee]

this youtube short was amazing for review. Thank you!

[@jarige4489]

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

[@MathVisualProofs]

Thanks!

[@treybell40501]

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

[@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.

[@barsbasaran8904]

such a clear explanation ! nice work

[@user-su3wk8od6m]

Best explanation on KZbin please upload the entire video of calculas...Your explanation is really great.......

[@nishantkumarsingh5002]

Yes

[@prajwalbhoite9865]

Beautifully explained, thanks

[@vladimirrodriguez6382]

Magnificent graphic explanation 👏👍😊

[@MathVisualProofs]

Glad you liked it!

[@user-ak7as2hi9q]

OMG👁️👄👁️ What a explanation

[@robertwaremusic]

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.

[@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.

[@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.

[@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

[@ceebad8985]

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

[@unknown-lg9oh]

Bro cooked my brain and ate it

[@Beegeezy144]

Beautiful.

[@Mmmmgh34]

Just WOW

[@TheSerpion148]

Very good❤

[@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.

[@omagoss]

Thank you very much

[@helldestroyer]

Thanks for nice video ❤❤

[@jonathanreynolds2625]

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

[@MathVisualProofs]

👍😀

[@user-yg2yi6gy3c]

Thank you so much it really helped a lot😊

[@pawanyadav3399]

Nice explanation🙏🙏🙏🙏 sir

[@MathVisualProofs]

👍😀

[@ndrcrypto]

amazing

[@antotot04]

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

[@elixpo]

Manim at its peak xD

[@vigneshbalaji21]

Nice explanation. Derivative is based on secant line

[@lory3771]

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

[@user-su3wk8od6m]

Love you from India.

[@MathVisualProofs]

👍😀

[@nishantkumarsingh5002]

Congratulations for the susses of Chandrayan 3...🎉

[@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

[@dominicellis1867]

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

[@TalSzor]

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

[@MathVisualProofs]

Glad to hear it!

[@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.

[@user-kl4wy5ih4g]

It's Lagrange's Mean Value Theorem

[@Drift1]

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

[@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?

[@TOUKAYSWISSI]

Good!

[@MathVisualProofs]

Thanks!

[@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

[@sumithadavid5841]

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

[@Cactly]

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

[@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.

[@Questiala123]

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

[@Miguel_Noether]

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

[@lahiru1k]

OMFG everything clicked!!!!

[@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

[@prithvisinghpanwar6609]

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

[@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

[@beanman7516]

Rolle's theorem lore

[@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).

[@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?

[@pureanimations4260]

What is an alarming wave called? A warning sine.

[@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

[@dranandamay]

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

[@rishabhbahuguna8903]

damn everything just clicked, im not even that good at maths❤️

[@amitvikramsinghparihar8241]

LMVT

[@koponstanley4]

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

[@ZAIKRO23]

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

[@decksforgg9883]

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

[@abdeljalilpr2033]

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

[@MathVisualProofs]

I’ll see what I can do.

[@mrawesome2704]

Are you on the manim discord channel?

[@MathVisualProofs]

Sometimes but rarely.

[@m7mdMAH5]

Bruh this video should be in every class that is starting derivative lessons, in our school they said "Limit", "Mr. what is Limit" "IDK it's just like that" Not even kidding

[@maki9462]

Nice

[@danangwiratama6887]

What apk do you edit math animation like that?

[@MathVisualProofs]

I use manim for these animations.

[@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.

[@joshuairvin9661]

Engineering student: x=a

[@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

[@nishantkumarsingh5002]

Are you Indian

[@MathVisualProofs]

@@nishantkumarsingh5002 I am not.

[@Malke864]

0:00

[@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

[@mohammadbajoouri568]

It is a+ or a-?

[@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

[@Fernandolorian_]

HOLY SHIT I THINK I GOT IT HAHAHA

[@christopherellis2663]

Pretty! But why would one wish to know that?

[@MathVisualProofs]

If you know the current state of a process and how it is changing, you can get a good feel for where the process will be in the future or where it was in the past. This is fundamental for studying anything that changes over time.

[@elreturner1227]

Not instant very very impossibly close but not instant

[@shubhamvishwakarma3629]

What if limit doesn't exists ?

[@MathVisualProofs]

Then the instant rate of change is undefined at that point

[@lanedouglas9297]

I do believe lim fubared me

[@11am2]

So f'(x) = 0/0?

[@MathVisualProofs]

In a sense.

[@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!

[@SpenceReam]

The word “instant” describes a concept that is without time. “Change” can only occur with time. The phrase “instant rate of change” is semantically nonsensical…

[@Boltkiller96]

i think he uses instant to refer to a very small time but yeah this is stupid

[@epicchocolate1866]

Well in other contexts it not. The velocity is the instantaneous rate of change of position

[@R_802]

Instantly rate of change? That's an oxymoron.

[@MathVisualProofs]

How do? There is the rate of change at an instant and there is the average rate of change. Calculus explains how to find the instant rate of change using a limit of average rates of change.

[@Werepizzaa]

Congratulations. You successfully made me understand this LESS. 0/10

[@MathVisualProofs]

Interesting. So how do you make sense of the derivative then?

[@abdulalialotaibi7062]

Not necessary for every day life

[@idlesquadron7283]

OK! a lot of things aren't and that's ok

[@burnulli1541]

perfect video ! Are you using manim for animations my friend ?

[@MathVisualProofs]

Yes I am!