Differentials and Derivatives - Local Linearization

This calculus video tutorial provides a basic introduction into differentials and derivatives as it relates to local linearization and tangent line approximations.
Derivatives - Fast Review: • Calculus 1 - Derivatives
Introduction to Related Rates:
• Introduction to Relate...
Local Maximum & Minimum:
• Finding Local Maximum ...
Mean Value Theorem:
• Mean Value Theorem
Concavity & Inflection Points:
• Concavity, Inflection ...
________________________________
L'Hopital's Rule:
• L'hopital's rule
Curve Sketching With Derivatives:
• Curve Sketching - Grap...
Newton's Method:
• Newton's Method
Optimization Problems:
• Optimization Problems ...
Marginal Cost & Total Average Cost:
• Marginal Cost and Aver...
__________________________________
Marginal Revenue and Profit:
• Marginal Cost, Margina...
Tangent Line Approximations:
• Finding The Linearizat...
Differentials & Local Linearization:
• Differentials and Deri...
Estimating Function Values:
• Estimating Function Va...
Antiderivatives:
• Antiderivatives
__________________________________
Final Exams and Video Playlists:
www.video-tuto...
Full-Length Videos and Worksheets:
/ collections

[@TheOrganicChemistryTutor]

Next Video: kzbin.info/www/bejne/hH2Tf3mMYrRrjMk Final Exams and Video Playlists: www.video-tutor.net/

[@heck6466]

aye bro u the best

[@tanwaduanhe7962]

Hello Good sir, i was wondering of which one i should start watching on your playlists about Differential Equations. Hoping i would get a reply, thank you.

[@superbutter476]

When a 10 minute video beats your whole week of class

[@somekindofname7859]

Yes

[@raleigh2747]

Well one reason why this is free and your university is not is because sometimes the information here is misleading. dy/dx is not just a quotient ( as Leibniz thought it was) of the differential of y over the differential of x, because the differential of y is dependent on the differential of x. It so happens that following Leibinz's notation, it "appears" that you can do this but really, this violates the fact that in differential forms have to be independent of coordinates. The proof for why dy = f'(x)dx is not as simple as multiplying both sides by dx. Try solving the proof yourself or look up the work by Edwin Hewitt, Jerzy Łoś, and Abraham Robinson

[@petergriffon8520]

@@raleigh2747 can you use this and solve every question correctly?

[@raleigh2747]

@@petergriffon8520 depends on what “correctly” means. If change in x is sufficiently small, then the approximation will be close to the actual value of f(x) at the point. However, if you are looking for an exact answer, finding differential equations by “multiplying” change in x to both sides will not work, especially when there are more variables.

[@itsCraftedPvP]

@Asa Harley or its a scam that actually hcks ur account

[@yousifss3783]

KZbin University is the best LOL. I’m spending money to go college where they teach you nothing like that, everything is complicated but when I come to this channel I get what I want from the first example. Thanks a lot🙏.

[@ghostfrom1950]

after getting my degree from Trump University, i'd have to disagree. Trump University trumps them all! LOL okay, bad joke. I actually do agree with your comment 👍

[@raleigh2747]

Well one reason why this is free and your university is not is because sometimes the information here is misleading. dy/dx is not just a quotient ( as Leibniz thought it was) of the differential of y over the differential of x, because the differential of y is dependent on the differential of x. It so happens that following Leibinz's notation, it "appears" that you can do this but really, this violates the fact that in differential forms have to be independent of coordinates. The proof for why dy = f'(x)dx is not as simple as multiplying both sides by dx. Try solving the proof yourself or look up the work by Edwin Hewitt, Jerzy Łoś, and Abraham Robinson

[@yousifss3783]

@@raleigh2747 Thanks for you explanation, I think we have an educational problems at the school, college or some book we use to learn or solve a problems, I have this question going on in my mind every time I learn something for example when my professor asks to answer a question about Maclaurin series, the issue is not really in how to solve the equations the Issue why I'm solving this what is the benefit, where I'm going to use it, give me a reason why I have to learn this not only coming to the class and wasting my time and you are not going to explain to me how the math you are teaching me is going to help me in my future. I have been asked this question by my classmates multiple times, and my answer was I don't know. And here when I started to look up every topics in what, where, when and how I'm going to use the math I learned in school. 🙂

[@raleigh2747]

@@yousifss3783 I think the reason why teachers often don't say why a student is learning something is because the answer really wouldn't benefit the student. Take this as an example, Algebra student is learning about linear equations. Although linear equations have many applications, there really is no need to go soooo far in depth as algebra teachers do, it would seem. But the answer is really, algebra students learn about linear equations for two reasons, it easily demonstrated the basic concepts of algebra, but really, its so that when they take calculus, its so that they understand tangent lines, and linear approximation and their proofs. But think about it, if a student asked, "why are we learning so much about lines?" and the teacher told it like it is, "so that you understand tangent lines, and linear approximation and their proofs in calc." the student would go uhh... okay, with no real increase to their motivation to learn it. unfortunately, in math, sometimes you gotta learn it with no real understanding of why you are learning it at the time. The understanding will come later.

[@yousifss3783]

@@raleigh2747 Yes for sure specially when you finished calculus and you think I finished calculus, but you realized no Static, Electric and Dynamic etc, are bringing me back to where I started which is algebra, for me I deal with equations as puzzle to solve and it is quite fun, for some students no I don't want to deal with math. I mean yes I struggle and when I struggle and I don't easily give up I keep search the information on the internet because. But no one wants to search or try. They want someone to feed them calculus which is what I'm doing right now with some students who are seeking for help, but they don't realize that I was struggling like them one time and asking the same questions and whenever they ask me I just say you have special tool called internet use it and everytime you feel like that you forgot something go back to your notes or to the internet.

[@beepsheep5954]

This is the hardest part of calculus fck differential. I'm amazed to those people that can understand this.

[@user-kg2ks8vk9z]

couldn't agree more it sucks Nobody's explaining the intuition too, they are just throwing already proven facts

[@bpavankumar9597]

​@@user-kg2ks8vk9zwatch professor Leonard's video for differential in calc 3 playlist.

[@coldshock5181]

​@@user-kg2ks8vk9zwhat do u find hard about it?

[@xtv_]

Thank you so much! 1 example here explained the 2 hours of lecture from my professor. God bless!!!

[@mariosspyrou1054]

The videos from 2006 are very good

[@user-wr8yg8ix6r]

LOL

[@an240x]

They are really helping

[@lizzyberg1082]

i know what you mean man!! that add makes me embarassed!!

[@damienfernando1553]

@@lizzyberg1082 lol, don't be. That's a VERY stupid ad for sure

[@learnwithsalim1228]

yes lmao !

[@eduardovaldez7830]

Bro i have an exam in 2 days, u are a literal blessing to us humans.

[@timjoyalle318]

How did the test go?

[@destroyer5620]

@@timjoyalle318 unlucky no reply lmao

[@elladre137]

hi how did the test go 😍

[@Hypnotic.-.]

I’m in precalc and I watched this for fun lol I know it gets harder but you made it seem so easy. I understood all of it and was able to do your examples on my own. I wish you were a teacher in my high school 😂

[@alexandrestamkos7488]

My boy right here is the TOP G of calculus. Man I love you

[@ian-hm6cx]

this guy deserves a space in heaven specially reserved to him

[@mangalover8764]

Thank you so much! You're our hope in passing calculus especially this time of pandemic

[@jbonceu2457]

Its crazy how all of this relates to primarily understanding the SLOPE which we all learn in algebra 1. Slope is change in y/change in x. dy just means change in y, dx is change in x. Derivative (dy/dx) then means we are finding the slope of the equation.

[@ExpungedFunkyFriday]

This guy explains Soo good that I literally understanded everything in the first minute

[@jalisabroussard8245]

Hi, your videos are extremely helpful. Is there a way you could record with higher audio volume? I always struggle to hear your audio clearly and turn my volume up all the way.

[@eljefea2802]

Buy another pair of headphones.

[@BarnesWelding0609]

You may also be able amplify it through your devices bluetooth settings. Or the speakers settings

[@BluesB0x]

@@eljefea2802 lol not helpful. what kind of headphones? if op were to invest in better headphones, like you vaguely suggest, it would be even quieter due to a likely higher power draw. A DAW or amplifier would be much more helpful and actually increase the volume ;)

[@andrewsciencetube3828]

all videos on this channel are what I need to understand. I hope in the next few days I can be equal with my high school teacher by using this tutorial as the main helper.

[@raleigh2747]

Unfortunately you wont be "equal' with your high school teacher because dy/dx is not just a quotient of the differential of y over the differential of x, because the differential of y is dependent on the differential of x. I'm sure your teacher knows this. It so happens that following Leibinz's notation, it "appears" that you can do this but really, this violates the fact that in differential forms have to be independent of coordinates. The proof for why dy = f'(x)dx is not as simple as multiplying both sides by dx. If you want to be equal, try solving the proof yourself or look up the work by Edwin Hewitt, Jerzy Łoś, and Abraham Robinson

[@andrewsciencetube3828]

@@raleigh2747 ok maybe you are right so i should correct my word " i can go adequately....." but you have to always remember that there are some students beyond their school teacher. because when you have a real interest in math you will read more and more than even your teacher.

[@elladre137]

Did you surpass your teacher?

[@simpleinformationhub8553]

Good job I always found your videos when I searched.

[@MacdonaldNkhoma-vo5gx]

You really don't spend your time for nothing we are benefiting a lot from your services❤❤🎉

[@georgesadler7830]

Professor Organic Chemistry Tutor, thank you for a short and awesome video/lecture on Differentials and Derivatives in Calculus One. This is an error free video/lecture on KZbin TV with the Organic Chemistry Tutor.

[@saddamkasumo927]

You are the best thing to ever happen to us .. I have an exam in 2 minutes 😃

[@joshuawillams1865]

Same

[@elladre137]

Has the test started yet?

[@FataIIity]

I have a midterm in a week with no idea how to do anything and now its 2am and here I am watching organic chemistry tutor

[@argie5697]

Fuck it.Coz of ur wizardness, i also recommended you to my friends and classmates who struggled a lot in mathematical subjects such as Calculus. Everything I am looking for is in your channel, that's why when i search something, i always look for The Organic Chemistry Tutor having a black background number thumbnail. Thanks a lot, youre helping me pass this smester. Youre really a big help specially this time that we are set to new normal. Youre my teacher, not my online modules. heartheart

[@zachh6868]

How can a 10 minute video teach better than a 40 minute video lecture?

[@shivanielitem6533]

You help me survive my math class everyday, Thank You So Much!

[@abdelrahmane657]

Totally agree with Super Butter’s comments. 👏👍🎓

[@mallninja9805]

What does "the differential" mean. "...and dx = 1/4" - why? What does it _mean_ to set dx = 1/4? Where does it come from? Is it something you can graph? WHAT DOES IT MEAN?

[@ayeshaafzal4884]

This is hands down too good

[@hanadiyousif5637]

In 1:51 how did you find that 3x

[@guliyevshahriyar]

Thank you very much for precious content

[@XxHXRxX]

I've learned one thing. The proximity of a result, compared to what's understood is acceptable.

[@zulaikhabatool3467]

So much helpful video 📸

[@mohammadamiw]

It was really good ❤ thanks 🙏🏻

[@chriswilliams5291]

So delta y and dy are similar values when delta x is small but grow further apart as delta x becomes a bigger value? Are delta x and delta y used for applied mathematics in the same way that derivatives are?

[@arashfrz4053]

God bless you❤

[@zakariya5460]

this is so easy

[@platypusih8u830]

kinda confused, what is the difference between dx and delta x? what is delta exactly (talking about the triangle one not the delta-epsilon)

[@telutron9755]

Amazing sir

[@princyshilshi8480]

Why can't teachers explain like this

[@tutstorial8474]

i thought dy/dx isn't a Fraction??

[@abdulsalamolayemi9388]

Please I need a video on first principle differentiation

[@ukjfx]

Thank you 😊

[@god8511]

What does the number 0.1 in dx=0.1 represent someone help please

[@BangMaster96]

But, delta x -> 0, wouldn't dy = 0 then, because you multiply the derivative by delta x ?

[@raleigh2747]

Yes exactly, this is one reason why dy/dx is not just a quotient of the differential of y over the differential of x, because the differential of y is dependent on the differential of x. It so happens that following Leibinz's notation, it "appears" that you can do this but really, this violates the fact that in differential forms have to be independent of coordinates. The proof for why dy = f'(x)dx is not as simple as multiplying both sides by dx. Try solving the proof yourself or look up the work by Edwin Hewitt, Jerzy Łoś, and Abraham Robinson

[@user-kn8ff7oq6w]

good math thanx

[@airplanefood6121]

thanks

[@Amir4v]

oh my god thank you very much wow :)

[@ShiroKage-h8v]

so what if like y=x+5ycos(2x)

[@ytman-lq2mj]

Nice

[@phamhuutri1996]

so what is the difference between derivative and differential ? i am getting mixed up between them

[@kristeldempseydeguzman8]

DERIVATIVE of a function is the rate of change of the output value with respect to its input value, whereas DIFFERENTIAL is the actual change of function (got these info from google)

[@Boog1137]

In the scope of this section, you could think of the whole derivative as the term dy/dx and the differentials are the individual dy and dx seperately

[@tutstorial8474]

but isn't it dy/dx not a fraction ? but why does it becomes dy bg just multiplying dx to the equation?

[@TheNightmare150]

I have a question: What happens when you got dy=xdx and u pick x=0 and dx=1. Theoretically delta y shouldn't be 0 but in this case it would be. Or am I getting something wrong?

[@shreycrescent]

you could i would assume take x=1 and dx=-1

[@comicsconerr]

Thank you have an exam in 20 min

[@VentiVonOsterreich]

It's been 2 weeks, how did it go

[@maryrosesaldua7107]

Smooooth

[@ardenburns1719]

wow, i wish we had learned this earlier, it makes alot more since this way. only thing that im confused about now is when to use dy/dx or just dy?

[@Evgenii-fr7eb]

I come here for explanation about derivatives and differentials but instead I've got 10 minutes video where guy solves some problem, why

[@ume6864]

Whatvis the meaning of it

[@jtak]

thank u for ur videos! please speak a little bit louder though :" sometimes i have to turn your vids to the highest max

[@ahmadal-khaldi2663]

How come I get 3.33333 when I put 1/2*Sqrt9 times 0.02 in the calculator, as seen in the last example

[@Hypnotic.-.]

2 years later but uh 1/2(sqrt(9)) is equal to 1/6 and then multiply that by 0.02 and you get some number idk

[@usctrojanfreak]

My exam is in 9 hours LOL

[@ThatDrummerFrank]

I have never seen a differential be assigned a numerical value before. In all of calc I, II, III and diff eq. Are you sure this is okay to do? Usually dx, dy, danything represents an infinitesimally small change in whatever value the differential is. Where did you learn this? If it's mathematically legal, then it's news to me.

[@ericfarmer5715]

Dx is the differential of x and it is mathematically equivalent to the change of x or delta x for some interval (x, x+ delta x ) the differential of x and delta x are equal dx= delta x

[@coep_leader4898]

I agree- delta x and delta y is the notation for finite increments

[@ipodtouch470]

As far as I know this only works for local linearization were Delta x = dx and Dy aprox = dy

[@sevrothegoblin5212]

When assigning dx to a value it is a representation of linear approximation

[@mryup6100]

I know that for sure it is illegal mathematically in some areas.

[@babrakazizi5878]

What is dy and dx?

[@deathrider365]

Dy and dx is dy/dx split up. You multiply dx to get out from below dy. It is implicit differentiation

[@iboa6938]

@@deathrider365 so it's like f(x) and g(x)? I never heard of dy/dx ?

[@risalia7638]

ibo a no, dy/dx is just the notation you use when you differentiate something. It can also be written as f’(x), for example. However, as you advance in calculus you tend to use dy/dx a lot more and ditch the other notation to manipulate your derivatives for problems such as these.

[@raleigh2747]

@@deathrider365 dy/dx is not just a quotient ( as Leibniz thought it was) of the differential of y over the differential of x, because the differential of y is dependent on the differential of x. It so happens that following Leibinz's notation, it "appears" that you can do this but really, this violates the fact that in differential forms have to be independent of coordinates. The proof for why dy = f'(x)dx is not as simple as multiplying both sides by dx. Try solving the proof yourself or look up the work by Edwin Hewitt, Jerzy Łoś, and Abraham Robinson

[@user-kn2ub2cj8z]

💛💛💛

[@zhandoshumyrbek9814]

5:44

[@user-kn2ub2cj8z]

💛💛💛💛

[@justusfrimpong809]

Godbless

[@cyvenfx7271]

What the hell that's so much easier

[@user-kn2ub2cj8z]

💛💛💛💛💛💛

[@tibeihahowillis5836]

Does anyone else feel complete when he taps his calculator

[@arvinbm6243]

Hmmm...

[@sebastiangiray3614]

Compute dy and Δy for y=ln(x^2+1) as x changes from -2 to -2.1. can someone help me? coz when i solve delta Y i cant punch my calculator ln(-2.1) - ln(-2) because it gives math error... hope some one can help me pls coz i cant sleep without figuring this shit out XD

[@myst5454]

But what the fuck does dy mean? I get how to find it but what does it meannnn

[@PardeepSingh-jh6ou]

Square root of 0.037

[@jesusc0der]

0.192353840617 Approximately.

[@asrafialmamun5767]

Wrong explanation in deriving differential. First you differentiate " lnx" w.r to x. Thant means dy/dx=1/x After that you multiplied both sides by dx and here is the wrong explanation you've done. Here d/dx is differential operator which is not a fraction. So you can never multiply both sides by dx. Please give the correct explanation.

[@user-hm6rm5qm2s]

甚至让我一个英语口语一般的人听懂了。。。

[@sarahjaneimad7103]

Je suis nul en math

[@user-kn2ub2cj8z]

💛💛💛💛

[@user-kn2ub2cj8z]

💛💛💛💛💛💛

[@user-kn2ub2cj8z]

💛💛💛💛💛💛

[@user-kn2ub2cj8z]

💛💛💛💛💛💛

[@user-kn2ub2cj8z]

💛💛💛💛💛💛💛💛