❖ The Chain Rule ❖

Подписаться 1,4 млн

Просмотров 1,2 млн

50% 1

📚 Mastering the Chain Rule: Essential Derivative Technique Explained 🧮
Looking to master one of the most important derivative techniques in calculus? You've come to the right place! In this video, I’ll break down the chain rule - a vital tool in calculus used for taking the derivative of composite functions. Whether you're prepping for an AP Calculus exam, taking first semester calculus, or just sharpening your math skills, this tutorial is perfect for beginners and those seeking a refresher.
🚀 What you’ll learn:
The formula for the chain rule (without proof) and its intuitive breakdown.
Two easy-to-follow examples to help you understand and apply the chain rule in different scenarios.
Key steps: differentiate the outside function, evaluate at the inside function, and multiply by the derivative of the inside function!
Looking for more advanced applications? Check out my other videos for deeper dives into complex uses of the chain rule and other calculus concepts like product rule, quotient rule, and implicit differentiation!
👍 Don’t forget to like, subscribe, and hit the notification bell for more math tutorials! Let’s build your calculus confidence one derivative at a time. 🔔✨
Watch now and master the chain rule to tackle any calculus challenge with ease!
#ChainRule #Calculus #Derivatives #MathTutorial #LearningMath #APCalculus #Mathematics #StudyTips #DerivativeTechniques #MathEducation #CalculusConcepts #Differentiation #ChainRuleExamples #ProductRule #QuotientRule #ImplicitDifferentiation #MathHelp #STEM #STEMEducation #MathLessons #DerivativesExplained

Опубликовано:

30 сен 2024

Ссылка:

Скачать:

Готовим ссылку...

Добавить в:

Мой плейлист

Посмотреть позже

Комментарии : 496

@patrickjmt 8 дней назад

Hi all! Wanna help a RU-vid education OG? Please post comments, questions and anything else on your mind in the comment section! so, don’t forget to LIKE, THUMBS UP, and SUBSCRIBE! I’d appreciate it greatly as it helps me :)

@kiely2851 9 лет назад

Patrick for president

@patrickjmt 9 лет назад

+nemo i'd be a terrible president.

@h2opolo433 9 лет назад

+patrickJMT still better than trump. thank you so much for these videos

@MrThatsYe 8 лет назад

+h2opolo433 Nah Trump ftw. Democrats put up a socialist and hillary benghazi clinton. Going to the repubs this time!

@heathermiller5413 6 лет назад

I like trump. I like Patrick too...

@ayushshah2103 6 лет назад

When do I use this and when do I use the product rule???!!!!

@sbk1398 9 лет назад

U should make videos on how to live. Ur teaching is so easy to follow. thank u

@ayushshah2103 6 лет назад

When do I use this and when do I use the product rule???!!!!

@patrickjmt 5 лет назад

Hi all! Please post comments, questions and anything else on your mind in the comment section! While I try to answer as many questions as I can, there are more questions than I can answer by myself so if you are someone who might be able to help, please do so! The community is so much better when everyone is involved and helping each other out. Our strength is our willingness to help each other! Also please feel free to like or dislike the video. Your feedback is always appreciated so that hopefully I can make my future videos the best possible! Thanks and happy studies!

@hayoo9470 5 лет назад

thank you

@parthgupta7515 4 года назад

log cosx

@syacks 9 лет назад

Explained the concept better than my math teacher and, more importantly, better than khanacademy! Thank you so much (:

@JohnnyYenn 8 лет назад

I came here from Khan Academy as well looking for a better explanation! :)

@alicelala2194 9 лет назад

thanks! Seems you're the only human capable of explaining this congratulations

@RawringShoelaces 9 лет назад

Your youtube videos are saving my math grades. You're the real mvp. :D

@drumandball 8 лет назад

You made a mistake in part one of question 4 when you said f(x)=x^2+sin(30)+2x^6....Just kidding. Now that I got your attention...thanks for making calculus easier.

@reereeg7325 8 лет назад

😂😂

@Sorites 4 года назад

Not gonna lie....he had us in the first half.

@dannymunoz8027 10 лет назад

Seriously I hope you're a teacher.

@TK_Cadence 10 лет назад

I swear calculus professors are so methodological to the point of having no relativity to people who do not understand mathematical terms for example dy/dx.. me (student) thinks "So this is like derivative of y over derivative x" when it is really derivative of y in respect to x. The terminology really leaves me in a derpy mindset in class and I'm like "what is this i dont even.." class ends and the professor sounds like hes speaking gibberish. PatrickJMT's real power is simplifying methodological language and at the same time making mathematics tangible to everyone. Your the man.

@oneonta310 9 лет назад

don't think of dy/dx as a fraction

@nicholasmaloof8378 5 лет назад

Agreed, the notation in math is pretty hard to overcome.

@nicholasmaloof8378 5 лет назад

I like to think of it as f'(g(x)) * g'(x). It's easier for me to visualize what's going on this way.

@Theluckyfrogful 10 лет назад

Finally someone I understand. Thanks Patrick!

@patrickjmt 10 лет назад

my pleasure! come back any time

@RexReedemer 13 лет назад

I love how my professor who carries a PH.D makes something like this seem so hard to learn. I thank Patrick for making it so easy to comprehend. Definitely will be doing better now on the upcoming exam

@patrickjmt 15 лет назад

i love pocky too!!! : )

@patrickjmt 16 лет назад

as i said, if it was the third power, you could just expand it out. if it is to the 30th power, you would not want to do that!!! so what do you do, the chain rule! : )

@patrickjmt 14 лет назад

@arturomlk92 to say they are useless is to go to the other extreme. they certainly are not useless. however for most students they do end up being irrelevant.

@patrickjmt 13 лет назад

@teh1337hackz0rz ha : ) trying watching videos on the topic your prof is going to cover before you go to class. you will get much more out of it!

@patrickjmt 14 лет назад

ok, if you say so. and 'your supposed...' is incorrect syntax. it is supposed to be ' you're supposed...' oh, the irony.

@patrickjmt 12 лет назад

sin does not mean anything. sin(x) does. so sin(2x+3) for example, is not a product at all. it is a composition.

@patrickjmt 14 лет назад

@flyingporcupine2 yes, every single person in usa is a complainer. everyone else in the world is sweet and wonderful.

@patrickjmt 14 лет назад

@mvenom101 i grew up in kentucky. i had to walk to school barefoot, get water from a well, and use an outhouse.

@patrickjmt 14 лет назад

@xlipsxdeceitx i also have just about everything u will need for bc, so visit often : )

@patrickjmt 16 лет назад

glad you like them! : )

@kristynicole6201 9 лет назад

Patrick JMT deserves a Nobel Prize... Ima email the committee right now.

@muhammadamirudin08 6 лет назад

Tq for voted me as nobel price winner

@shenrondragon191 6 лет назад

Kristy Hamlin yes literally

@patrickjmt 13 лет назад

@wh0iskarl now someone just needs to give me a few million dollar grant too :)

@patrickjmt 13 лет назад

@MultiKRINKELS yes, many people would do great if they had the same epiphany

@chrisdiamond5125 10 лет назад

God bless you sir

@patrickjmt 12 лет назад

@sprtrprs1134 an engineering degree is one worth paying for

@patrickjmt 12 лет назад

@thetman22 i am at least not the worst person on earth : )

@patrickjmt 14 лет назад

@mdxfeever333 if you take your money to the bank

@patrickjmt 12 лет назад

@chipuarbuu wonderful! however, some of the videos on here on youtube but NOT on the site just yet, so you may do a search here as well. otherwise, the calculus stuff should all be in order.

@patrickjmt 14 лет назад

@BXNYhardstyle you too hardcore for math!

@patrickjmt 14 лет назад

@BXNYhardstyle ya boy, you tell that math!

@the-real-zpero 10 лет назад

I love you.

@patrickjmt 12 лет назад

@kazam92 i agree: the chain rule is certainly the most confusing of them. the fun part is when you get to combine all the techniques, then factor and clean it up, etc.. come back any time! i have calculus playlists and extra stuff that i have forgotten to put in the playlists.

@patrickjmt 14 лет назад

good, then i did what i intended to

@patrickjmt 14 лет назад

@therock343 well, this is meant to be a basic introduction to the chain rule, not the hardest problem ever. i do have harder examples using the chain rule if you wanted to look for them.

@patrickjmt 13 лет назад

@FiresDoFly it might just happen!

@patrickjmt 14 лет назад

@collindh15 ha, wonderful to know

@patrickjmt 12 лет назад

@mmb314 you are very welcome : )

@patrickjmt 12 лет назад

@xo1k4 let me think about it...

@patrickjmt 13 лет назад

@lemmingsfly maybe he forgets!

@patrickjmt 13 лет назад

@babycakes00777 happy to help!

@patrickjmt 12 лет назад

@ShylockEffect my pleasure. welcome back and good luck in your studies

@patrickjmt 14 лет назад

ahahhahah

@patrickjmt 12 лет назад

@dollas608 it beats english

@patrickjmt 14 лет назад

@PhizzleOut no, i keep some airplane glue nearby for that

@patrickjmt 12 лет назад

yes, the title is not ' A Proof for the Chain Rule ' :)

@patrickjmt 12 лет назад

and?

@patrickjmt 16 лет назад

great to help! i will be in mexico in about 3 weeks! : )

@patrickjmt 12 лет назад

@vasemedroserii ha :) you did a good job trying

@patrickjmt 16 лет назад

yes, you use chain rule of composite functions.

@patrickjmt 13 лет назад

@jpmoench21 glad it helped so much : )

@iWINuLOS369 10 лет назад

This helped so much thanks!!

@patrickjmt 10 лет назад

you are very welcome!

@patrickjmt 15 лет назад

yes, i prefer this way toO! glad it helped

@Seekr88 12 лет назад

Patrick, I must thank you for creating these awesome videos. I'm a 30 year old returning student, and so I haven't seen much of this in quite a few years. I was really stressed out when I started my Business Calc class, and so I spent a great deal of time studying. I stumbled across your videos while looking for Math lessons on RU-vid. Thanks to your instructional methods, I am no longer worried and am really starting to grasp the material. Thanks for all that you do, sir.

@percyjackson7600 10 лет назад

thank u thank u soooo much... woah a left hander ... still ... epic ! XD

@malkotoPor4e 9 лет назад

You just facilitated my life! I spend 2 hours figuring out the crap written in the book, and i still couldn't do them. Thanks a LOT!

@aaronshenk 3 года назад

this was SO helpful. You saved my grade near the end of the semester. Much appreciated Patrick!! :)

@mmb314 12 лет назад

I just want to tell you how much I appreciate these videos! I hope you realize how much of a different you make - I would never have been able to pass my first semester of calculus without you. thank you so much!

@JerryBarau 9 лет назад

so this is what my Instructor meant?? it looked 20 times more difficult in class.

@FireVortex720 9 лет назад

Keep it UP, you rock Patrick!

@lisandrahernandez2614 10 лет назад

PatrickJMT is the real MVP!!!

@toadsworthrox 11 лет назад

Thank you for posting these. My calculus professor was getting really frustrated when I tried asking how to solve using the chain rule. It made absolutely no sense to me and it's my last math class I need to take. Thanks again for the help!

@jaidevmeena3986 4 года назад

differentiation of sin square(x square +1)...???

@rageplays8551 3 года назад

i wish i could hug you right now man , thank you

@azenethrivera6428 9 лет назад

LIFESAVER!! Finally I get it just in time for my final tomorrow Thank You!

@patrickjmt 9 лет назад

***** you are very welcome! good luck on the final!

@rookietastic 7 лет назад

x(secxtanx)+ sec(x)(1) = xsecxtanx + secx

@jitendrasharma4983 5 лет назад

Etna short video 😆😆😆😆😆

@juwonkim1837 4 года назад

the best teacher ever.

@patrickjmt 4 года назад

you are too kind :)

@rr78884 10 лет назад

thank you so much. you have helped me pass college algebra last semester and now you are about to help me pass business calculus. i love you!

@edimulo3903 3 года назад

Your writing is so neat

@MusicDJz1 10 лет назад

Lifesaver! Just started Calc 2 and forgot how to do a lot of the stuff in Calc 1 (took it 3 semesters ago O.o). I got this.

@SenLightyear 10 лет назад

Wow dude I am in the same exact boat! Godspeed!

@MusicDJz1 10 лет назад

astro_yesi good luck to you!

@narturo994 10 лет назад

***** Same situation here! This guy and WolframAlpha are the real MVPs.

@jlarellano7350 7 лет назад

you're a much better teacher than my teacher. I could hardly understand what she's saying.

@kowshikbhanu448 7 лет назад

THIS GUY IS HELPING ME TO DO MY HOME WORK....

@edgarb.6187 10 лет назад

Thanks man!!! Really need this for my AP Physics class.

@angelic2234 9 лет назад

Brilliant, it finally makes some sense. Thank you!

@yosuatanto 13 лет назад

you're lefty :D

@arunagupta2422 6 лет назад

After 10 years😀

@shivkumaryadav3607 5 лет назад

Good

@eclipse245 14 лет назад

okay...I'm in Advanced functions. i don't understand what derivatives give you? All it looks like is like you're still left with a super long function?

@Marbledberry99 6 лет назад

omg ... can't believe I understood this so fast .. GOD BLESS YOUR SOUL

@thepoorcapitalist 9 лет назад

THANK YOU SOOOOO MUCH!!! im in college at oklahoma state univerisity and you just helped me out a TON in my business calculus class!

@DevonMarks 9 лет назад

Hey Patrick thanks for the video. I have a question that I am really stuck with because of the log involved. Could you help me out? Determine dy/dx if y=(x^5)^lnx

@RocanMotor 13 лет назад

when you slid that paper down, for a second I thought to myself "I KNEW HE WAS MAGIC! LOOK AT HOW MATH JUST APPEARS ON THE PAPER! MAGIC!" Then I realized it was just a paper being slid down... regardless, I still think your a magician.

@jeveuxlesoleil 14 лет назад

LIKELIKELIKELIKELIKE. When you wrote down the fcn after 2:30 I literally squealed with happiness. I have one of those on a midterm review and the exponent at the end was driving me nuts. I was overthinking it entirely. Thank you SO MUCH!

@mvenom101 14 лет назад

Yay for free maths tutoring :) Im in australia in high school, and this helps soo much. so, now i can spend more time riding my kangaroo to school, and hugging koala bears. :)

@ZoeCalico 11 лет назад

Used to use your videos in high school. Five years later I'm doing diff eq my senior year, and I don't know what I'd do without these videos to brush up on what I've lost.

@samhouston1288 12 лет назад

I was getting the hang of derivatives, but the chain rule had me completely lost. Thanks for the tutorial. It was a ton of help, and now I understand the chain rule. :D

@MathMikie 15 лет назад

why is it called the chain rule it is compostion of functions it deals with the product ruledeals with products sum rule deals with sums but this one doesn't follow that rule

@victormendoza3295 7 лет назад

I would say 100 squeezed. 1 = f, 0= g, 0=g. Squeezed as in the outside is prime.

@Jarlzdotorg 9 лет назад

257; said x^3; meant x^2

@nixxanator 11 лет назад

Technically you can use the the chain rule for sin(x) since the derivative of x = 1 it would just be cos(x)*1 or cos(x). It's just one extra step.

@nadiabegum40 9 лет назад

Tq soo much u dont know how much u have help me to pass my exam..u r really great tanks again....😃😃😃😃😃

@Evarya 4 года назад

ur amazing. my textbook, professor, and khan academy all made it seem so complicated but you explained it so well. thank u :)

@Capon3d 13 лет назад

Thanks so much for this. The book I'm using uses some impossible notation (dw/dx=(dw/du)*(du/dx)) but this makes it so much easier.

@JohnNeri 6 лет назад

Thank you! You are helping my wife and me, right now. :)

@botanysilkiebreeders7732 6 лет назад

We going to uni baby! Thank you so much. missed a couple days (literally 4) and didn't study over the christmas break i had for my summer school and came back with 4 weeks left and feeling totally lost on how to tackle this but i feel like im finally catching up. thank you thank you thank you

@blinkatreyu 11 лет назад

You explain it so much better than anyone else thank you so much, your videos have helped me understand alot of Calculus :)

@SemiToneBlew 11 лет назад

Haha, you're waaay better than my Calculus Professor, I gotta thank you, from an F I ended up with an A+, thank you!!

@handlexz 10 лет назад

I'm pretty sure this is my first ever comment on RU-vid or otherwise. Tis a great day I found this video and thanks for helping me understand something my Calc teacher poorly handled for many a weeks.