❖ Understanding the Derivative: The Slope of the Tangent Line Explained ❖

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Understanding the Derivative: The Slope of the Tangent Line Explained
Description:
In this video, we dive into the fundamental concept of the derivative and its geometric interpretation as the slope of the tangent line. 📈
Ever wondered how to find the slope of a tangent line at a specific point on the graph of a function
𝑓(𝑥) without having two known points? 🤔 We explore this by using the concept of limits!
Join us as we:
Define the derivative in a clear and intuitive way.
Visualize how to approximate the slope between two points on the graph.
Learn how to make those points closer together while keeping one fixed.
Discover how this process leads us to the definition of the tangent line's slope.
This video focuses on building a solid understanding of the derivative conceptually, rather than calculating specific derivatives.
Whether you're a student, educator, or just curious about calculus, this explanation will help demystify this essential mathematical idea!
Don't forget to like, share, and subscribe for more math insights! 🔔✨
#Derivative #Calculus #MathTutorial #TangentLine #Limits #Mathematics #LearningMath #Geometry #FunctionAnalysis #Slope #MathEducation #CalculusConcepts #Visualization #APCalculus #StudyTips #StudentSuccess

Опубликовано:

13 окт 2024

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Комментарии : 506

@chickenzwings 9 лет назад

If these videos didn't exist I'd have had to take calc and stats over multiple times. You literally have saved me thousands of dollars and thousands of hours. THANK YOU!

@patrickjmt 9 лет назад

+chickenzwings in that case, you should head over to 'Patreon' and consider being a supporter. you can support for as little as 3 cents a day :)

@kimcasem 8 лет назад

+patrickJMT what is patreon

@kavan1773 8 лет назад

+Homo Erektus Well he did teach us something.

@phucdangchannel 6 лет назад

@@kimcasem he legit just told you what it was.Maybe this is why you fail your calculus class.

@kimcasem 6 лет назад

phuc dang Dang , u r phuc-in’ mean dude

@ticatacatic 10 лет назад

Me every 10-20 seconds: ...OHHH.......oh..OHHH!!!. thank you so much. Really.

@goriaakash 6 лет назад

dude 4 years later, its happening to me XD

@HDitzzDH 6 лет назад

Quite a satisfying realization isn't it? That happends to me all the time as soon as I truly understand a new concept within physics or mathematics, that's what makes me love it so much, for example all the formulas we have been using for years (not really understanding why) and then deriving it aka going back to the origin of that concept, I just experienced it myself deriving the quadratic formula which is based on completing the square.

@Shubham.Katyal 6 лет назад

same

@Parhoom 6 лет назад

Same 😂

@carayork2388 6 лет назад

@@goriaakash ffdhhrhdjdwjkcrufu the

@baykkus 9 лет назад

You talked about the secants and suddenly everything made sense before the end of the video. Such a simple explanation and I had been struggling for a long time to figure why the formula made sense. That's the power of a teacher who actually bothers to explain I guess.

@FlowerRFabulous 8 лет назад

i love you because of your simplicity YET thoroughness! thank you i been trying to figure out what a derivative was, looking all over the internet for a simple definition and you gave it to me!

@patrickjmt 8 лет назад

glad i could help :)

@julierimer4544 10 лет назад

You are an amazing teacher. Not only do you explain everything so well, you have such a calm demeanor that is conducive to understanding. I always understand the concepts after watching your videos. Thank you so much for helping all of us understand!

@patrickjmt 12 лет назад

glad you like the videos :) thanks for the kind words. be nice to my sweetie wife! i know she had to give tests back today and the first round is often a shock to most people. good luck and work hard!

@patrickjmt 12 лет назад

yes, there are quite a few videos missing from my website - it is a bit of a pain to keep updated. always best to check on youtube as well!

@ccg1994 13 лет назад

finally someone tells me WHY this is the formula, not just "this is the formula, memorize it & use it to find the derivative" Thank you sooooooo much!!

@110Turab 5 лет назад

Its 2019, after 10 years, still thanking.

@reithsymonds4517 6 лет назад

Don't watch this after a beer or two; You should never drink and derive.

@BangMaster96 5 лет назад

+Reith symonds What is a proof? A: One-half percent of alcohol.

@kemchobhenchod 4 года назад

so good. so good. especially because i'm drunk.

@sanchi7410 2 года назад

Yo this is funny

@rileydavidoff1929 9 лет назад

PERFECT explanation! If I hadn't have found this video, I would have no idea what to do for my calculus presentation. Thank you so much!!

@yukichancinnamonroll 10 лет назад

wow! for a moment I lost hope in understanding this. I was just memorizing the formula (the f(x+h)...) but when I was listening to your explanation and the meaning of the derivative function then everything just makes sense! thank you so much! you are better than this text book I have and even better than my teacher! thank you!

@andrewhorrocks8814 6 лет назад

My sentiments exactly!

@brooklnsummers3578 9 лет назад

Awesome explanation!! I'm a college student who has a professor who can't speak english, so this was great!!

@patrickjmt 9 лет назад

Come back any time!

@geraldmanalansan9733 3 года назад

this guy saved me from my calculus 11 years ago. I am one of your first subscribers. thank you

@techshiftz848 8 лет назад

The intuition behind this is pretty straight-forward. When I first saw this it was pretty weird, and I thought it was not even related to the Gradient formula. Great video Patrick!

@misty348 10 лет назад

'memorize it and arent quite sure where it came from..' - That was me before watching this

@ksfishchannel 6 лет назад

Maheera S same

@swati5667 10 лет назад

thank you man....love you..i didn't understood this topic in two years of my college and you explained it clearly in just 12:08.. mins..!!!

@itsyoboyak12 6 лет назад

swati nampalliwar same😢

@JFrazerful 12 лет назад

The roller coaster analogy for tangent lines was excellent. I've never had anyone explain it that way and it makes it quite intuitive.

@coreyewalsh 12 лет назад

I watch the ad's because you deserve to get paid for this. Also you've taught me more than my own professor. I just show up to class to save face. Thank you.

@JosefBorg 7 лет назад

The subscription I've given you is seriously the most worthy subscription I've ever given. Your explanation is flawless.

@patrickjmt 7 лет назад

glad i could help you out! :)

@fscmathsbymissmahrukh7492 3 года назад

thnku sir i really appreciate u ,,ur teaching method is very well good ,,,mostly teachers didnt teach subj of graph theory bcz its a very difficult and distinct object but i think u is the first person who teach us graph theory in better way again am very thankful to you from pakistan

@nickschor 14 лет назад

Where were you 30 years ago when I really needed you!!! Either I got a lot smarter over the years, or math educators have gotten much better. Thank you very much. Math ROCKS!

@akosiar15 6 лет назад

Hi Patrick. I just want to let you know that you are really awesome! I just recently passed my board examination for Electronics Engineering through the aid of your videos. Keep on making videos. You rock!

@patrickjmt 6 лет назад

congrats, that is awesome!

@lindsey8964 4 года назад

So I'm watching this... through my Calculus online class Canvas. Your videos are literally a part of the curriculum. And thank god for that, math class has never been more straightforward and easy to grasp. Thank you.

@patrickjmt 4 года назад

thanks a bunch! glad the videos are helping, tell your teacher thanks for using them!

@nandhiniraja3523 7 лет назад

you are really awesome. At the beginning of calculus in my college,i was really scared on how i am going to understand it but you have made everything very easier. I have seen all your videos on limits and now started with derivatives. U are a life saviour.. Thank you so much sir.

@patrickjmt 7 лет назад

my pleasure! :)

@selvam2487 11 лет назад

this video is really awesome. for the last 10 years I have memorised this formula without trying to know what it is all about. now I don't have to memorise it anymore. thank you Mr. Patrick.

@patrickjmt 14 лет назад

@Matsuyama1234 glad u like it: : )

@louisli1962 11 лет назад

This is what my teacher trying to teach us for weeks, and you just explained everything. thx a lot

@ejsg34 13 лет назад

thank you! patric!! you saved my life! My professor couldn`t explain the definition of derivative clearly like you!

@patrickjmt 12 лет назад

always happy to help out a nice person such as yourself ;)

@eyorokon 8 лет назад

This was brilliant. Amazing explanation and the use of pictures/graphs really helped a lot.

@omnnnooy3267 9 лет назад

with knowing that i am not perfect with English but i really understood everything you said , it's really clear and great ,you are the best math teacher ever , thank you man .

@jonathanbiedermann2608 4 года назад

I don't have a whole lot of money, but you've helped me way too much for me to not even try. Thanks again

@patrickjmt 13 лет назад

@falconpally any time!

@warrensnook9435 4 года назад

The roller coaster analogy is a really clever way to explain the concept!

@patrickjmt 12 лет назад

@Achab94 yes, i am paying someone to update the site,but she is a busy college student so it will take some time

@AlwaysBeMyThunder21 13 лет назад

You have no idea how much you've helped me understand my calculus homework! Don't know if you actually read you're comments but I just want to say THANK YOU!

@ramirosalas20 12 лет назад

your videos have saved me in all my college math courses up to now.. just wanted to say Thank You!

@LinaLuckway 11 лет назад

Patrick, you are awesome! I am happy that I found this site! I will recommend your website to my college peers this summer. Thank you so very much!!!

@samanpaydar4415 5 лет назад

for first time in my life I completely understood meaning of derivative thank you very much

@goriaakash 6 лет назад

you're the ultimate life saver, im taking an accelerated calc class and they dont teach all the basics and reasoning behind the formulas.

@MidwestTh 12 лет назад

Your a beast at math. I have watched many of your vids for many of my courses like but not limited to Statistics, college algebra, finite math, and currently calculus for business. Thanks alot

@siyayas9134 4 года назад

I'm cryin that i found this at my 18 cuz this is really helpful

@yihsss 11 лет назад

thank you so much for making this and also other tutorial videos....it is 1 am + and i am headache about derivative that i learnt yesterday in school...but your video really clear those questions appear in my mind...how amazing is your teaching method...I love your explanation!

@mashaalleyne 8 лет назад

Thank you for your simple, yet effective explanation. Helped so much!!!

@steveswanson4152 10 лет назад

Thank you! Awesome explanation! Only possible with someone with a creative brain of a left handed!

@muhammadericali 11 лет назад

I "liked" this video before even watching it.. I just knew I'd find it helpful.. and what do you know.. God bless you Patrick!

@Zelda1990s 7 лет назад

One of the best learning experiences of my life... AND IT WASN'T PAINFUL FOR ONCE!!!

@MouradBENKADOUR 7 лет назад

Great explanation,finally I understood the definition of Derivative, Thank you so much.

@SpacySpaceCadet 13 лет назад

Thank you thank you. I stared at my calc book for about two hours, very very helpful. I think you may save me for my calc test.tuesday!

@uniqueversalunicorn2412 6 лет назад

Finally I understood this concept in different in full

@carlosng500 11 лет назад

all i can say is that you are much better than professors in college....i almost watched all of the videos of the topics that were taught in class

@amyparola 9 лет назад

What a wonderful video! I loved it. I watched your videos a lot while in Calc 1 and 2 a few years back. I since have graduated with a degree in secondary math ed. I have been asked to teach AP Calc in the fall and am very excited. However its been awhile and am using the summer to bring it back! You explained this so well! Thank you

@chriscollins5320 9 лет назад

Wow, this very well done. Thanks for explaining how the secant and tangent lines are correlated! Will subscribe.

@MinaBolis9 10 лет назад

Great Teacher ! I skip my calculus class and watch your videos ! You explain better than my teacher :D

@patrickjmt 14 лет назад

@VictorAndScience yes, it is the same

@patrickjmt 13 лет назад

@jayboyfloyd glad it helped. if you get it the first time, then i am a super star

@draxxillegaming 11 лет назад

You are the reason why I never pay attention in class. A year in a half and going strong! I made a 103 in my stat class thanks to you!

@siyiai8668 6 лет назад

my god this is my first ever youtube comment and it is given to u, thank you so much for these videos in calculus, you always know where i am puzzled and the solution is as beautiful as a scratch to the itching spot

@patrickjmt 6 лет назад

glad i could help :)

@MrAceBry 11 лет назад

geez you're amazing. totally. you should be paid for all this. THANK YOU!

@TheEclipsedsun 12 лет назад

YOU ARE BRILLIANT. I already had a good grasp on this lesson, but after this video i feel like a freakin math wizard. thank you!

@isabellarestrepo5582 7 лет назад

I hope you are still making videos. You have no idea how much they've helped me!!!

@patrickjmt 7 лет назад

i still am :)

@patrickjmt 13 лет назад

@ShakkIsLife if h -->0, the points get closer together

@Warhawk40Champ 11 лет назад

Im in seventh grade taking algebra 1 and got really bored of solving quadratic equations so i started learning about derivatives. So now i feel smart as hell and i wish this guy was my teacher... He is so thourough in helping me make sense of this

@FuneralMarky 13 лет назад

Thanks I understood it on the first sitting, if only my school teacher was like this.

@Jezebel1115 8 лет назад

OMG!!! Thank you for explaining the difference between the tangent and secant line so clearly!!! I finally get it, and it makes sense!!! DAMN!!!

@narutouzamaki9376 8 лет назад

this guys teaches better than my teacher

@BlkDiesel 12 лет назад

As always your work is splendid. informative but not over anyone's head. Makes the concept simplistic enough so any laymen can understand it. Thanks for your dedication, passion and time spent.

@XCracer2014 11 лет назад

In 10 minutes this video taught me more than my calc teacher could in the entire class hour. Thanks!

@patrickjmt 13 лет назад

@StrawberryMarshmalow keep watching! : )

@23youwatch 8 месяцев назад

takes me back to my college days you were the only teacher we really had!

@20jakubukaj08 12 лет назад

Excellent - these videos are an enormously helpful resource to me. Your hard work is very much appreciated.

@LKordich 8 лет назад

I have been trying to teach myself calculus because my teacher likes to read the book to us. That doesn't help me understand the material. I have been watching your videos. You have helped me to understand more in this less than 13 minute video than I learned yesterday in 3 hours of class and 3 hours of office hours. Now hopefully I can put it to use and remember.

@patrickjmt 8 лет назад

+L glad I could help. Come back any time!

@LKordich 8 лет назад

Thank you.

@saymaislam1057 8 лет назад

You are so amazing! Please keep making videos because they are so helpful. You make it easy to understand math even for people like me who suck at it. Please just keep doing what you are doing because it is helping soooo many people.

@lilitkirakosian8540 5 лет назад

This was the best explanation of any math problem ever. Thank you!!

@natash179 13 лет назад

WOW, you're awesomeee, couldn't ask for a better explanation. Thank you!

@sriharisha251 6 лет назад

theres no such video explaining this clearly. thank you sir.

@patrickjmt 13 лет назад

@CristinaPeter411 happy to help! : ) tons of calculus stuff, so visit often and tell your friends!!

@EricMarinelli 13 лет назад

You are an amazing, amazing person. While my teacher isn't bad, I wish my teacher taught as well as you! I totally got it the first time I watched it.

@22burst2020ddsspec 12 лет назад

Thanks so much bro. Teachers don't realize the bloody importance of emphasizing on the formulas they throw at you. I think when you can visualize them it allows you to have a better understanding so that you can expand on it, and use your own brain...

@FRSUPRA 12 лет назад

Great videos, way better than my math teacher (who just gives answers to problems). Completed two assignments already thanks to your guidance.

@vr_bob 6 лет назад

Thorough and simple. Great explanation!!

@sameerpokhrel4379 5 лет назад

This video clears all my confusions. Thank you

@rancegarrett3696 7 лет назад

Awesome! I'm a high school senior but I'm taking pre calc at school. My boss is paying me to learn calculus on the job. At first it was alien language but I'm getting more understanding everyday. I'm just preparing for college as well. Engineering is life!

@dighbijoysamaddar459 9 лет назад

this is really wonderful for students who really want their mathematical foundation to be strong

@LariosGiveNoFucks 8 лет назад

Love your videos my dude! You've explained it way more clearly than my calc professor.

@StrawberryMarshmalow 13 лет назад

I wish I had your as my maths teacher! I'm finally beginning to understand derivatives and limits!

@yokizhang8740 4 года назад

thank you so much, this so helpful even after 10years

@Mahmood- 7 лет назад

You are our light bro, thanks. Understood it perfectly

@Weejee456 12 лет назад

Patrick I have been watching your videos since my 9th grade Geometry class. I am now in Calculus and in my last year of high school, I really appreciate the time and effort you put into teaching us. Thanks and see you in college =D

@AngryArmadillo 11 лет назад

You can find other points on the function by plugging in any value for x and evaluating the function. These points can then be used to calculate the slope of a secant line.

@ДФҜя 7 лет назад

I have taken calculus in both languages, Arabic and English, and in different countries too. But I could not grasp anything, even though I love Math and I had a faith that one time I will get to the hang of it, which turned to be by your excellent methods of illustration. Thank You So Much. I wish all instructors share the same skills and techniques you use.

@matthiasheinrichs2499 11 лет назад

I love how in almost every video you mention that "again, this idea can be kind of confusing..." freak yeah it is, calculus in general is rather confusing to understand at first! But we appreciate your efforts.. :) By any chance any tips for properly understanding the book Thomas's calculus early transcendials and it's way of posing questions better?