2.1 - Definition of the Derivative

[@andrewsailo3925]

This is what I am looking and searching for...By far the best explanation of derivatives

[@Name-jw4sj]

By far the best explanation in KZbin of the definition of a derivative!

[@athulyadevermadam1169]

exactly

[@maddoglord]

Went through an eng degree heavy with maths, never could visually picture a derivative. 10 years later you've done it for me in 10 minutes. I will draw this to explain it to people 1000 times over. Thankyou.

[@geraldillo]

I sort of grasped the concept of calculus but I never really could picture what happened with the formulas or how a derivative looked like. Excellent explanation; thank you very much!

[@gregstenger848]

This is very well explained. This is the best way I've seen this explained. Great video!

[@jayjayTT868]

Simply speaking, this is the best video tutorial I've seen on the Definition of the Derivative. Well done #rootmath...

[@condor3902]

This was awesome! Even 9 years later this video is super useful! Thank you!

[@aihamkadiri4992]

yah calculus isnt going anywhere lol

[@tohidalamkhan4081]

Best explanation ever, I watch lot of videos in yt for this but I can't understand and also our teachers never teach us in this manner , now my concept is crystal clear , If I will be teacher then I will teach my students in this manner. I will never make them face those problems that I faces now.

[@Rajesh_KC_911]

*Best teacher i have seen so far... thank you so much man you made my day.*

[@ramesh.programming]

Lol you should too make more videos.

[@Rajesh_KC_911]

@@ramesh.programming videos of what brother 🙂❤

[@hayasarah12]

You are the definition of the word legend mashallah

[@pairot01]

at my school we definded the derivative in a point to be f'(a) = lim (when x-->a) [f(x) - f(a)] / (x - a) is there only one valid definition or are both correct? does one have an advantage for teaching (and learning) derivatives?

[@Foretolds]

Awesome Video!Concise and easy to undererstand. I now fully understand derivatives!

[@anakhalal5803]

I know you won't see this comment since this video is 9 years old (hope you doing well). But this is incredible, just incredible. I was confused about this concept (which I tried to learn in my native language) but I can't seem to understand it, and here you are, ecplaining it in English and I understood it perfectly!

[@rootmath]

I still read the comments! Glad the video helped!!

[@sneakypress]

@@rootmath lim (at the limit) h --> 0 . So, it’s not that ( h approaches zero ) as in ZERO being the origin of the x - y co-ordinate axes ; the ZERO refers to the (absolute) minimum VALUE at what you call the ‘point of tangent-cy’ . Is that right ? Is that how to say it ?

[@athulyadevermadam1169]

finally, i found what i was looking for.. best explanation of the slope of a curve. thank u very much.

[@akshaypatil834]

Hey that was an amazing explanation about derivatives!

[@jimkeller3868]

I apologize for the length of this post. I have struggled with trying to explain the Derivative in purely conceptual terms. Here goes: The tangent line embodies the rate at which one variable "y" changes in relation to a change in another variable "X". The tangent line at a point actually cannot exist, since at a point (an infinitesimal) there is no change in either variable. However, the secant line intersecting a curve at two points is NOT an infintesimal but an INTERVAL and so DOES have a slope. The secant, is an AVERAGE rate of change of one variable with respect to another OF THE FUNCTION over an INTERVAL (represented by the two points of intersection). One of the points of the secant line, that intersects the curve, is the point with which we are trying to establish the slope (the rate of change...the relationship between how "y" changes with respect to "x", the TANGENT line). The closer we bring the second point of progressively shorter secant lines towards the first point, the closer (better) the AVERAGE rate approaches to the "true" value at that first point, and the closer the secant line becomes tangent to the curve at that point. For example, if a driver slams on the brakes before hitting a tree, he is decelerating. However, at the MOMENT of impact there is no CHANGE in either distance, time or speed (the true definition of a moment) - like the slope at a POINT...it's non-existent. But let's say you want to know the ACTUAL speed (not the CHANGE in speed) at the moment of impact. If we take the change in distance averaged over the one second before impact (like the secant line...two points, the final point, and the one second before final point), we get a an average speed over THE FINAL SECOND, (change in "y" over change in "x", distance over time = speed). But remember, the car continues to decelerate during this final second towards impact, so the speed averaged over that final second is not an accurate account of the speed at the moment of impact. However, If we now take the AVERAGE speed over the final .5 secs, then progressively over .1 .01 .001 .0001 and .00000001 seconds, (two points getting closer together along a secant line) we approach the actual value at the POINT in question (the tangent line). The average speed the car was traveling during the last .000000000000001 second, is going to be close enough to the actual speed at the POINT of impact. Two points .0000000000000001 second apart IS STILL A SECANT LINE, but very closely resembles the tangent line. It has to APPROACH the tangent line WITHOUT actually getting there. Why? If it does get there then the change in time = 0 and the change in distance = 0, therefore, there IS NO SPEED - a bit of a paradox. Averages are TWO POINTS (slope). The "actual" speed is as close as you can get to ONE POINT (the derivative), without actually getting there, that is, as "x" APPROACHES 0.

[@maktub_txt]

This was so s so well explained. Literally my entire assignment in 10 minutes. Thankyou!

[@Twinsell1256]

Thank you so much, I've been so stressed because our teacher gave us this IMPOSSIBLE assignment that she didn't even explain. I've been searching all night long for an explanation, this helped me so so so so much

[@muhammadsohaib5455]

after watching many videos,i was just confused about this term but your lecture really helped me to understand it.Great method,Thank you.

[@aphysicistsdiary]

Please tell me about the software u use for recording and managing the lectures. Thank u in advance

[@sushilbalakrishana8419]

Derivative in purely conceptual terms , thanks a lot very nice of you .

[@Vikermajit]

Awesome explanation...did not understand secant line...now I know...tq for the enlightenment...

[@WRONGTURN69]

wow! I wish my professors explained it like this! Thanks! :)

[@monatoshbarman11]

Thank you Sir.. This is one of the very few best explanations of derivative..

[@kestutisa3826]

Very well explained. Showing the essence of the problem.

[@VideoSiteAccess]

Literally THE best explanation ever!!!!

[@lowlightevangelist9431]

You taught me the limit concept. Thank you.

[@gamewarriorman7587]

This is very very well explained sir lot of thanks for help

[@TerrexoDesign]

Very nice explanation !

[@seang9678]

so good your saving my life here.

[@mitwalimirgani]

Best explanation about derivative

[@Stringbean421]

wow,..really great explanation. Thank you.

[@nassimaissaoui2177]

wow that's so amazing explanation, how can someone dislike this :o

[@shahulsayyed9052]

Why we can't just project the different points on tangent on the x and y axis to get their coordinates and then use the formula for slope?

[@urielalfaro9716]

Great video bro, thanks so much (y)

[@emmanuellopez6744]

hello what is the name of the software you use to write

[@rootmath]

I use GIMP, its free and open source

[@GuyFawkess]

that was great thank you very much my teachers never talked about that

[@kvenkatrao5141]

Great

[@endergaming7252]

what do you use to draw

[@livewirelive8256]

However since h is never zero you will never be able to ascertain what the slope at x is .This is important when extreme dense data is used. For example : when programing a chip to shoot down a high velocity missle.

[@PedroRodriguez-dl5yt]

Excelent explanation. THANKS

[@rootmath]

You're welcome, thanks for the comment!

[@muhammadandikalesmana1708]

Thank you very much for amazing explanation the definition of a derivative video, sir!

[@zahraafiras4696]

Thank you for this explanation👍

[@JasonRichardTesch]

Ok, so x+h and x just has to be really close to the same number. and in the general cases we assume they are infinitesimally close.

[@vineethreddy.s]

Great explanation sir.... Very nice......

[@RF-fi2pt]

The paradox is we see the way to 0/0 indetermination as dt->0 , but suddenly Calculos solve the indetermination at the instantaneous point. The answer to Calculos rigorous solution is because the straight line is the only function where ds/dt=s/t. As the tangent straight line have one point arbitrary small common to the function, with value s/t ratio, we know that value with the ds/dt ratio, even with Big ds and Big dt. Genial and rigorous jump as others in Math :-).

[@lavodky4775]

thanks a lot ... it makes me understand derivative

[@mschindee4997]

Wow, very well explained. ❤️

[@serinacat4781]

Great explanation

[@vineethreddy.s]

Nice explanation sir.....

[@alfadex50]

great explain tnxxx

[@thelearningcentre]

best video i have ever seen

[@Galenus0]

Very good explanation, thank you! :)

[@themegaruler]

Ur the best dude Dropped a subscribe for such a great help

[@Sandysan11111]

why you are taking the lim where h towards zero it should be towards the x value

[@rootmath]

You can think of h as the distance away from x, so as h goes to zero the point goes to x.

[@robertmurto2142]

I wish I could have watched this video before I took Finite Mathematics. I would have made so much more sense.

[@sivakumard9947]

Great Thank you sir

[@مهندعايد-ز8ذ]

it is best explanation

[@20javiero]

Great video

[@rakeshkchauhan]

The difference between infinitesimal and zero is not explained or even attempted

[@rootmath]

Thanks for the comment. Infinitesimal may be a useful intuition for some but mathematically it's not very helpful. The rigorous way to deal with the concept is through limits, no infinitesimal needed.

[@rakeshkchauhan]

@@rootmath In mathematics helpfulness is of no consequence. Every thing must be proved rigorously and in multiple dimensions. May be the postulates can be exempted but they are so intuitively correct that students don't really demand for a proof. Coming back, my school teacher said - this is the definition of differentiation ! What the hell? Am I in a literature class. This torture doesn't stop there. Soon comes probability and it is not proved and later... Now it seems to me pretty clear that such truncated studies or "accept it for the time being" are not good for the development of reasoning and therefore the development of themes with some historic perspective should be elaborated to quench the thirst of rationality. Thanks.

[@irappapatil8621]

A good question,by Rakesh.Actually this diffrence formula y2-y1/x2-x1 or f(x+h)-f(x)/h itself is inadequate or it is not a ge neral formul.This formul explains only the product of a constant and a variable,for e.g f(x)=cx.but it fails to explain products andpowers of indeterminate quantities.Unfortunately this inadequate formula is arbitrarily manipulated to as if it is the real formula.All these efforts stemmef from Leibnitzians who found the conclusions reached by Newton are true but his method eas false.There fore they wanted to devise thised deceptive and misleading method.Newton's Method of Fluxiond is the only true method,but nonr is able to understand it. I have written on this ,explained and verified method of fluxions and submitted for publication.Let us wait for it.

[@stimulantdaimamld2099]

excellent

[@mr.president1705]

Thank you

[@nagendraagrahari2239]

Bahtrin

[@divyanshumishra24136]

thank you so much

[@aparnasahu7120]

Thank u so much.

[@NandishPatelV]

Very lucid thnx

[@vishakhasah8310]

Thanks 😊

[@dthomas4614]

Thank you.

[@srmarasini1946]

You are awesome

[@suhadalkhafaji8995]

Finally i understood

[@faheemullah5574]

thank u sir

[@jiannisDimi]

As x approaches x, not zero...

[@drofeng]

As h->0?

[@martinnieva8484]

I understood it more in here than in a class of Khan haha

[@jaafar3811]

that was great

[@ezrimata4540]

Y'all should speed it up at least once

[@pola0614]

^But we’re not going to give up^

[@dimkayilrit2606]

Great content