Applying First Principles to x² (2 of 2: What do we discover?)

[@HarshDave009]

I just binged watched 4 of this guys lesson just for fun. What an awesome teacher. Someone get this man a medal.

[@jordantrevayne]

Harsh Dave I think they got him a few...and awards too

[@pyromaster10000]

Intuitive and easy to follow.

[@sonyxperia7881]

Same

[@shreyasp3287]

Get this guy sheilds , medals, trophies , Nobel's , everything

[@anesumukura7312]

😅me too

[@karanag21]

I am 37. Why the hell am I binge-watching this strange yet wonderful teacher explaining things that I don't have any use for?

[@peteralexandruhautelman8946]

I've been struggling for years to understand the meaning of the derivative, asking all my teachers to explain it to me. And now, you have shed light on this subject. Thank you, Eddie! Math really is fascinating! f'(x) is equal to the gradient of the tangent wtf

[@masum_pori]

wow...just wow. You're the only person on youtube who can explain with reasoning. you have to finish all the topics before I finish my high school. So please keep uploading.

[@sunnyblaze4912]

I love how the crowd is excited and really into it.

[@sieg624]

I have been through Highschool loving maths all the while, learning only the method not the reasoning. Thank you for giving me the reasoning =D

[@andyony2]

Its very interesting to watch the Video as a german math teacher because of the difference in the terms: We dont use "turning point" as you do: In germany turning point refers to turning the direction of the curve - Inflection point in english _ as you mentioned in your second example, where you dont have a turning point. We call your turning point a "extreme point" or in Detail a "low point" . It is very interesting to see the difference in our languanges, I often think, the english terms are more accurate and intuitive to unterstand than our german terms!!! I am glad to find your channel by coincidence. Its very inspiring, so I get new ideas for my classes and teaching method :) Thank you!!!

[@Obyvvatel]

They are called extremes in polish too

[@milly4543]

Turning points can be local maximum or local minimum points but they can also simply be turning points. Consider a graph that has multiple turning points of different value as well as points of inflection. You wouldn't be able to call all the turning points extremes as only one is a local maximum/minimum. How would you approach this using German terminology?

[@argonwheatbelly637]

Are you referring to saddle points? I.e. (sgn(f'(x+dx)) != sgn(f'(x-dx))) | f''(x) = 0

[@samk6042]

We also call the turning points the vertex

[@xapie128]

Another term that's different in the U.S. is Eddie says "f-dash" where we say "f-prime" (a dash is a horizontal mark similar to a negative sign or a hyphen, but slightly longer).

[@isalutefamille]

55 yo. Woke up watching this because the learning never stops regardless how old you are.

[@gman8648]

57 here and I couldn't agree with you more.

[@chipcurry]

Try 73. I took calculus in college as an elective. But I went a different direction and majored in sociology, now work as a musician. But I did like the calculus class. I still like it.

[@nhatnamtrinh5017]

I'm 46, and wish that someone had taught me this way when I was in school.

[@vodkacannon]

chipcurry Nice. If your head hurts, it means you’re learning and growing.

[@vodkacannon]

chipcurry You can figure out the secrets of the universe with math. It makes life satisfying.

[@Guide504]

More like Eddie WOOOOHOOO i finally get it... What an awsome young teacher. Brushing up my calculus as part of mediation.

[@tristanmoller9498]

God, I want to learn calculus from you man! You think you’d ever publish a playlist from your lessons? I’d even pay for it.

[@kelleybryant9351]

For anyone interested, you can go to mrwootube.com and look for the lesson videos. It's all links to playlists of his youtube content, but in the order you would take it in his class. It's also freely given. misterwootube.com/2020/03/18/lesson-videos/

[@raabia936]

@@kelleybryant9351 God bless you

[@robertrobert5832]

@@kelleybryant9351 thanks a lot,,

[@chetna938]

That's actually will be cool

[@TheJanstyler]

I've had all of this in school before and was (and still am) very good at implementing it. But after watching this video I honestly feel like I understand it way more than I did before. If every maths teacher were like you, maths would be a vastly more popular subject.

[@lowiehojas5525]

so much "AHA!" moment for me, shows how much i don't know and just learnt from you. Thank you so much!!

[@sciencethings5731]

I finished high school a couple of months ago and this guy has me watching math for fun. I had an aha moment when I finally understood what this stuff was all about

[@clemverpomtato]

the last part was a huge tease. this is better than most series i watch

[@ricardogoncalves1607]

Eddie Woo thank you so much for doing this. You are a hero. The world needs more people like you. Only education can help us do and get better!

[@siklair5295]

Hi, I love your videos! They are so interesting, I already know everything you talk about but the way you talk about it is just fantastic! If every teacher taught like you mathematics would have such a good reputation! Love u!

[@semmering1]

Best explaination ever seen -.great teacher, respect!!!!!

[@rukonuzzamanbd]

Just mind-blowing ❤️

[@kevongunning2309]

this dude thought me something that a teacher take 2 terms to teach me. he is great.

[@MaxTooney]

I wish I had gotten such a concise explanation by some who obviously ENJOYS teaching when I first took this 'subject' over forty years ago :-(

[@argonwheatbelly637]

This is a joy; a guilty pleasure, like watching a cooking show. I'm enjoying the cheerful teaching method, and it inspires me to do even more to help my children fall in love with math.

[@perplexedmoth]

Best instructor I've seen hands down. Just wow.

[@lowiehojas5525]

Thank you so much Eddie for the videos you upload. I am not a smart man, and i struggle to learn something by just "do this because that is what it is". I need to know the fundamental reason why such thing is being done. Your way of teaching is excellent for me.

[@cindygirlification]

A Wonderful Generosity of spirit shines through in Eddie’s teachings ! Thank you mate 🙏!

[@michaeligwe6406]

You are a great teacher Mr Woo. I just watched your videos for fun but you make Mathematics so much more meaningful and fun.

[@yashlakdawala7232]

Just amazed! In school I just knew derivative of x^2 is 2x, now I know why. It solves a lot of problems ahead.

[@JeremaeFlores]

I passed calculus not understanding a thing. I wish this was how it was taught! Your students are blessed

[@m.moonsie]

So how did you do that exactly?

[@kebrl]

​@@m.moonsie It's possible to memorize derivatives such as x^2 > 2x (and pass the class) without actually understanding why it works that way.

[@75pdubs]

@@m.moonsiememorize and regurgitate. It’s the way schools work here in America.

[@mirkkuffs]

THANK YOU! When we had this in math class the teacher was just like "Here's this formula. Put the numbers here, it works." and I was completely clueless. Thanks to you I actually understand the subject!

[@darmstadtium9558]

What's the formula?

[@mhellden]

Finally I got the basic Calculus... Thank you

[@asrobolord3153]

u r the real best teacher who I know of

[@thepanther1728]

i wish there was a playlist from 1 to infinity, from eddie woo :)

[@egregiouslytalented2381]

i am 13 and learning integral calculus becuz of u eddie .god blast the people who have disliked the video.

[@userzero]

Have not practiced calculus for several years and the fundamentals went out the window. Here I am required to take Calc 2 and this is helping with the refresher. Thank you.

[@adilmurad5028]

Great, learning with fun

[@narimafanficfan]

(I am the farthest from Math any human could be, but still I UNDERSTAND WHAT THIS WONDERFUL TEACHER SAYS!!!!!! its a miracle!!!!!!!!!!!!) Bless you man,!!!!

[@ezekielward1183]

I've learnt a lot in that little space of time than I learned in a hole semester. Good job

[@rosellaaj3709]

ngl its kinda amazing that we can find the gradient at ***any*** point on a graph simply by taking the derivitive

[@ashmita183]

Binging on this like it’s Netflix

[@davidgyang7817]

wow!!!,this is wonderful,interesting and insightful.

[@tieman3790]

Wow ive done primes so many times and just now i know where it comes from. It makes so much more sense now

[@ArhamKhan05]

Sir you are doing a great job

[@giuseppe3010]

EXCELLENT EXPLANATION -- other math professors should watch this video !!!

[@Kindly365]

Finally I understood what s the meaning behind using lim x tends to 0 in front of functions. Wish i had such teacher ..

[@biktolia_7223]

I'm still stuck but thats probably a me problem, your lessons are amazing

[@Alex-eo1to]

This guy is so much more engaging and insightful than Sal Kahn.

[@logicalstrike4772]

Thats Australia for ya

[@prateekdhingra6957]

Exactly!

[@AnshulRaman]

*Khan There is a big, big difference between Khan and Kahn

[@nobod354]

@@logicalstrike4772 Australia doesnt exist dawg

[@Libegfrat1]

You are great. Your passion passionates

[@waqasahmad6737]

I WISH I had a teacher like him growing up.

[@nameunimportant1073]

No wonder Mr Woo has over a million followers - he is such a great teacher!

[@ojassingh8313]

Very helpful, thank you so much sir for your kind efforts. I am satisfied the most after watching yours explanation I express my gratitude from India.🙏🙏

[@pratyushjena282]

It's so awesome I never thought that I can understand this topic you contradicted me.😁😁😁😁😁

[@day_lenh4243]

This is the only person who can really teach well

[@christianjohnflores4966]

day_ lenh i agree

[@khasheshaikh210]

Amazing those guys are lucky to get a teacher like him

[@rajmiglani4159]

Not netflix but your videos are a cake to binge 😀

[@abderrahimboutat9860]

U helped me a lot remembering math...thank u

[@davidyim5019]

Is there another video after this one or this is it for this equation? I now understand why I had to take calculus back then. GREAT INSTRUCTION!!!

[@fmhqbattousai]

I'm about to go back to college after 11 years -- the students he's teaching in these videos are in 11th grade. I can understand some of it, but I definitely need a more basic math course (or 20) before I take calculus haha -- I feel incredibly dumb.

[@ufukakkaya9534]

Bro, even the fact that you want to go back to college provea, that you're not dumb at all! Just put effort into this along the way and I believe you'll make it! 💪🏼

[@lazy_apple4893]

Im 10 and my mom is soo happy that i know calculus now 🤣🤣

[@Jrloveish]

So I’m retaking calculus, from the comfort of my phone. You sir are an amazing teacher.

[@theoharisgkagkos528]

I love your videos❤

[@JohnVanderbeck]

Took me an embarrassing long time to realize "gradient" is what we call "slope" in the US

[@jimmorrison4291]

6:45 It finally clicks into place! Good feeling

[@cynic150]

What an interesting piece. It takes a long time to get going at the start, very slow and lethargic. But later on it is really exciting.

[@alanbrooke144]

I did calculus up to 2nd year at university, and no one ever bothered to explain what it was, or what purpose it served - ‘just learn the rules’. No wonder I never really understood it.

[@petertran5419]

Reading these comments here it confirm how great my h.s. math teacher was. Mr. Sadlowsky, Columbia Heights H.S. MN class of 90. He basically taught us calculus in first principle. Derivative, integral, etc.... all with the limit of h approaches zero.

[@75pdubs]

You’re lucky. First principles is the way to go rather than the silly memorization our schools typically teach.

[@snehashissarkar9259]

I really hated calculus but damn after your vdeos it's actually interesting in school and college we were only told to mug up the formulas and apply them which I royally failed at but now I think they will be a lot more easier to remember

[@MJ-iy4fb]

Eddie, you're a master at explaining math. Nice job!! I enjoyed your lessons. Thank you for sharing.

[@milindbordia]

Lit fam thanks

[@lucbauer]

i finally understood what derivatives mean graphically!

[@RetroGamingClashOfClans]

ok so that's how you get the equation of the velocity vs time from the position vs time graph.. in my physics1 class the graphs are always given so I always wondered isn't it gonna be hard to get the equation of that velocity vs time graph when there is a uniform acceleration ( > 0 ) but now ik you just substitue the position vs time equation into the first derivative

[@ggbond942]

Sir reminds me of why we need teachers

[@rdkinley]

wish i had had lecturers like this 50 years ago at UCNW Bangor 50 years ago

[@AakashVaish]

I wish I could meet him in my school years!

[@sarajones7180]

Any chance you can tell us what book you are using or is there a link available for the exercises?

[@rabiueldodo7019]

How I wish you were my college mathematics teacher

[@AkuroGames]

7:07 (gotta remember this!!)

[@hbruwnghnem3112]

Sir, cannot see and read the small writing on the blackboard.

[@Mariomation3275]

how do i find the playlist for this thing?

[@thethaledwaba8561]

Back to the basics.

[@gman8648]

Me too Harish!

[@cadmiumbop]

You can tell this guy loves maths. It is all in his eyes

[@Vasilioo7]

I have never understood small rocks of measure but think I’m understanding😁

[@israelRaizer]

What happened at 6:34? Did someone bump into the camera and the video had to be stabilized?

[@tristanmoller9498]

What would f'(x) look like on the graph for f(x) = x^3 It’s incredible now we have graphs to describe the exact steepness of other graphs!

[@tristanmoller9498]

Or as an equation?

[@finlaycampbell3234]

Tristan Möller the f’(x) = 3x^2. The x value (which represents gradient on the f(x) graph) is always positive but is getting ‘less positive’ up until y=0, and then gets bigger.

[@Mot-dh5sx]

If you want to find another derivative you can always go on symbolab.

[@alwaysthelight]

Mr Woo makes you think why you are using formulae, not just plugging things in.

[@reznovvazileski3193]

Hmm this got me thinking why it doesn't go steeper visually but does go steeper numerically. Giving it a shot I came to the conclusion that phi = arctan(y/x) so then |d/dx * phi| = |d/dx * arctan(y/x)| = 1/(x^2+1) which goes to zero for x -> inf.

[@JT-wk9sf]

Hey what happens next!! Where is the 3 of 2???

[@saadehmarsel]

When we sub x^2 for F(x), how do we sub x^2 for F(x+h) ,, wouldnt that be (x^2+h) ?

[@LukeRaus]

Hi Marsel, figured I'd have a go at answering your question despite it being 7 months old. In the function definition where we say f(x)=x^2, we could use anything else instead of x: we could say f(c)=c^2 or even f(?)=?^2. The function is simply saying that we square whatever term we input. So if that term is (x+h), we can think that ?=(x+h) so since f(?)=?^2, we get f(?)=(x+h)^2. Again, we simply square the input! The confusion arises because Eddie uses 2 x's: by inputting (x+h) as x, it seems like he's saying x=(x+h). The important thing to realize is that these x's have nothing to do with each other! The x in the function definition simply represents "whatever term we input" and has nothing to do with the x on his graph.

[@justinatienza4494]

did you just refer to the original function of x^3 as the vanilla version lool genuis at its finest

[@mikumikumiku]

KZbin's auto generated subtitle was able to differentiate between Stationary and stationery.. amazing..

[@vagabondmanish4097]

👍👍👍

[@UmarAlFarooq]

Awesome explanation!! I got like 90% of that.

[@paulynnlrobertson]

We want the tangent, not the secant! Great work.

[@yksnimus]

whats the vid next to this?

[@misterwatson3337]

there is some evidence that calculus was first used by pythagoris(it may have been one of his contemporaries). But I have seen the evidence.

[@saxbybolton-johnson5288]

Would someone be able to explain to me why f'(x) = 2 x 1 at 6:39 . Where does the 2 come from?

[@kebrl]

Since f'(x) = 2x when the x (input) value is 1 we get: f'(1) = 2*1

[@rafaelbentes2989]

i love you

[@brianacorrielus8890]

In the U.S we say the slope more often😂

[@Musicrafter12]

My experience matches yours, but at the same time I do find myself preferring gradient since the definitions remain consistent as you get into multivariable calculus and start calculating 3D directional gradients. The gradient vector function of a parametrized multivariable vector function works out to be the same thing as the classical "slope" in fewer variables.

[@rhpmike]

So... can't teachers just watch this guy before their lesson and teach this way?

[@rinawmatlau1105]

Damn i want to turn around time by knowing this so bad

[@startuckval5198]

6:34 camera bop