Seriously, I would fail calculus if it were not for these videos. I cannot tell you how large of a service you are doing the student community by posting these. You have my deepest gratitude. I'd be happy to donate resources for your services here!
In this example you have applied the chain rule once. In some tests it requires you to apply the chain rule until the inner function is at its simplest, so very basically you are left with one x and a number. That is why its called the chain rule: because you can continuously apply it until you reach 0.
@@kimmarch90 It's been a year but if it still confuses you, it makes more sense when you think of the exponent*thederivative has some constant (A) and apply the d/dx Af(x)=Ad/dx f(x)=A*f'(x) rule. Then repeat the chain rule.
i agree with all these people who find this video soooooooooo helpful....i was trying to study this in my calc1A text book and the longer i tried to understand the chain rule the more confused i got. this video makes it so clear. thanks a lot.
+Khan Academy I just wanna say you are doing a marvellous job explaining the content of all your videos. You are the reason I could intricately understand certain concepts. Thanks a lot!! xoxo
These videos are amazing, I love how you are direct and straight to the point wasting no time at all. I am definitely recommending you to all of my friends :-)
You didn't confuse me, very clear!! thank you. I am a maths tutor and I usual only tutor year 10 and bellow but I was recently given a year 12 student who "cries when it comes to methods, the whole class does" (His words!) this will greatly help me get him to understand this!!! so thank you again!! :D
I've been out of school for about 5 years now. Thinking about going back tor a mathematics degree I never finished as a Computer Science major. I have to say, Khan is more coherent than most of my university professors I've ever seen!!
I'd give you 5 stars but I can only give you a thumb up. Thanks for explaining stuff in such a clear manner. You are going to be the sole reason I pass AP Calculus.
i been struggling in calc this whole time n i tried my best to learn my text book n the more i tried the more it confused me but after watching your videos for d first time itself it all made sense...THANK YOU SO MUCH.. I DONT KNOW WHAT I WOULD HAVE DONE IF I DIDNT FIND YOUR VIDEOS. :)
i love you. u are so much better than my math prof who just doesnt even make sense. i think u are going to be the only reason y i pass my midterm tomro. THANKS. u are doing an amazing job. keep it up!
Ok, my only question is, in the second example, when deifferentiating the largst bracket, why wouldn't you then multiply by the derivative of the inside? so where you have 3(3x(-2)+(5x(3)-7x)(5))(2), why dont i need to then multiply by the derivative of inside the bracket?, so, 3(3x(-2)+(5x(3)-7x(5))(2) X (3x(-2)+(5x(3)-7x)(5)
thank you so much for doing this! i can never learn properly in school because my mind wanders a lot, and if i miss even 1 thing the teacher says, i won't understand the entire lesson! but i can always replay videos and that's the best part
I know man!!!! I hate that shit, when you get taught something in a simplistic fashion, and they expect you to know what to do when it becomes this complex!!!!!
Excellent explanation and I learned a lot, so much that I could catch a mistake, somebody also did before me. Final answer: [(15x^2-7)(5)(5x^3-7x)^4-6x^-3] (3)[3x^-2+(5x^3-7x)^5]^2
very good, i want to point out just one thing , in the last problem you need to put a parenthesis "or brackets"in [(15x^2-7)(5)(5x^3-7x)^4-6x^-3] so that way it would be [(15x^2-7)(5)(5x^3-7x)^4-6x^-3] (3)[3x^-2+(5x^3-7x)^5]^2
Confused me? My teacher confuses me! This is what teaching should be, taking time to explain the steps. My teacher taught us the chain rule in one class (2 hours). The next day we were given an in class assignment with the chain rule, but with fractions and rationals. In my head, I was saying ''God help me''. Teaching is an art, and thank god there are still some good teachers out there sharing their knowledge for free. Thank you.
2:25 "To the minuuus 8." I don't know why, but something about the way you said that was hilarious. Thank you for making these videos and being awesome.
He does that, but in reverse order. Where the brown in the last line is the derivative of the large bracket, the pink times the green accounts for the derivative of the inner portion you mentioned: dy/dx (3x(-2)+(5x(3)-7x)(5). The light blue is the derivative of the last remaining inner portion: dy/dx (5x(3)-7x)(5). I was taught to tackle the outside first, so his method appeared a little backwards to me at first.
This review well for me learning for others is great your sessions are well timed so never to long and easy to follow. I forgot how long these calculus problems can get. If I remember correctly some problems can get extremely long.
so to find derivitave of "blob" raised to a power you just pull one "blob" out and find the derivitave of "blob" and then multiply it by the derivitave of what you are left with when you pulled one "blob" out. Is that right?
I appreciate the work done and time given in producing these videos but Good God - perhaps we could all chip in a few quid and enable Khan to purchase some more refined writing and video software. In other words, I suspect that many whom wish to learn Maths pause the video, in order to follow it through and reckon it in their own heads. But its almost impossible to see what is written.
Omg... I actually got that.... if my University professor had attempted to teach me this then there is no way in hell i would have followed so clearly.
wow. amazing. thankyou! my $4000 tuition money for the subject would be better off with you...atleast itd pay off by me actually learning something. thankyou soo much
My god I feel so sorry for the people in the comments here that have teachers who don't explain it this way! My math teacher was excellent and she always made sure to go through everything step by step, even when we had two months less than everyone else to do calc (IB is hard). I'm glad these videos are here for people who aren't lucky enough to have teachers this amazing in school.
Yeah man, you are awsome, thank you for your lessons !!! Thought I can't learn these things :-D, but its quite clear now, you saved me a lot of time...
does the first chain go on forever? How do you know when to stop? lets say you stop at the answer where the 2nd term is raised to the -8. so, you could keep subtracting one indefinitely?
I noticed you wrote a ^2 instead of a ^1, you were showing that there is a ^1 but when you copied it down in yellow you mistook it for a 2 :) Thanks for this anyway
Normal teachers: explains the simple questions and leave us with the hardest
Khan: explains the hardest and makes us feel that calculus is fun
But calculus is fun, indeed :/
@@r4fa3l59 these q isnt even that hard
Facts
My teacher said we'll have to do 12 functions inside of 1, though. Lots harder.
This site has improved my grades immensely for several challenging college courses. Thank you.
B E I take calculus and vectors in high school
Sterling Archer cool no one cares
@@sterlingarcher3981 r/IAmVerySmart
@@JamesTownsendJian bet, I am an 11 y/o who learned this for fun without problem, redditor
Seriously, I would fail calculus if it were not for these videos. I cannot tell you how large of a service you are doing the student community by posting these. You have my deepest gratitude. I'd be happy to donate resources for your services here!
My prof is great but hearing someone else explain it is just that much more helpful.
I swear I will donate as soon as I can as you deserve it khan academy.
did you donate now ? after a year ?
@@deltaschool4302 All in due time.
Did you donate?
Did you😁
did you donate tho
The highest quality content available in the lowest quality
graphics!!
In this example you have applied the chain rule once. In some tests it requires you to apply the chain rule until the inner function is at its simplest, so very basically you are left with one x and a number. That is why its called the chain rule: because you can continuously apply it until you reach 0.
So basically is the derivative = derivative of the inner function * exponent! ?
I have been noticing this too. My professor takes steps so much further and expects us to do so also. :/
First order derivative. Only higher order derivatives require iteration of the chain rule.
@@kimmarch90 It's been a year but if it still confuses you, it makes more sense when you think of the exponent*thederivative has some constant (A) and apply the
d/dx Af(x)=Ad/dx f(x)=A*f'(x)
rule. Then repeat the chain rule.
Back in the days of 240p...
Back in the days of 1080p....
@@rayhanmansoor2951 though they have now come back!
To be honest it looks much more fun, entertaining, and captivating.
1925 views by today, in one year, this will have 1 million +
Thanks, Sal!!!!
i have never had a teacher this great... bless you man, you're just amazing at what you do
im spending a fortune at university and learning 1/5th of the information i learned in this video
big ups :) and a BIG thank you!
i agree with all these people who find this video soooooooooo helpful....i was trying to study this in my calc1A text book and the longer i tried to understand the chain rule the more confused i got. this video makes it so clear. thanks a lot.
A kid with rudimentary math skills can learn this!!!
Are you a some sort of math GOD?
+Khan Academy I just wanna say you are doing a marvellous job explaining the content of all your videos. You are the reason I could intricately understand certain concepts. Thanks a lot!! xoxo
These videos are amazing, I love how you are direct and straight to the point wasting no time at all. I am definitely recommending you to all of my friends :-)
Mr. Khan, you are a beast! The way you explain is amazing.
Good video but you should add natural logs, logs, trig fcns as well, that's where the chain rule raps a chain around your head.
amazing... I watched these videos non-stop, and now I'm going to be ahead in calculus! (I'm in precalc)
Thanks so much!
You sir, are a hero above all heroes.
You didn't confuse me, very clear!! thank you. I am a maths tutor and I usual only tutor year 10 and bellow but I was recently given a year 12 student who "cries when it comes to methods, the whole class does" (His words!) this will greatly help me get him to understand this!!! so thank you again!! :D
I have spent days trying to learn this and you taught it to me in 10 min. Awesome videos. Thanks for the help.
Thank you always, Khan Academy! You are the best!
FOR THE MILLIONTH TIME, THANK YOU !!!!!!!! .
I've been out of school for about 5 years now. Thinking about going back tor a mathematics degree I never finished as a Computer Science major. I have to say, Khan is more coherent than most of my university professors I've ever seen!!
still saving lives, i tip my hat off to you sir
Hey how's is it going pal
After 7 years
I'd give you 5 stars but I can only give you a thumb up. Thanks for explaining stuff in such a clear manner. You are going to be the sole reason I pass AP Calculus.
I tried watching a different set of lectures first and they made next to no sense, but everything you say makes absolute sense! Thank you!
i been struggling in calc this whole time n i tried my best to learn my text book n the more i tried the more it confused me but after watching your videos for d first time itself it all made sense...THANK YOU SO MUCH.. I DONT KNOW WHAT I WOULD HAVE DONE IF I DIDNT FIND YOUR VIDEOS. :)
I'm 16 and i understood this rule.
Thank you so much.
I watch your videos because they are entertaining.
The derivative of f(x) in the first example looks more complicated than f(x) to be honest...
the world needs more people like you, sal.
you are just changing the world man.That is something you should be proud of
i love you. u are so much better than my math prof who just doesnt even make sense. i think u are going to be the only reason y i pass my midterm tomro. THANKS. u are doing an amazing job. keep it up!
Ok, my only question is, in the second example, when deifferentiating the largst bracket, why wouldn't you then multiply by the derivative of the inside? so where you have
3(3x(-2)+(5x(3)-7x)(5))(2), why dont i need to then multiply by the derivative of inside the bracket?, so, 3(3x(-2)+(5x(3)-7x(5))(2) X (3x(-2)+(5x(3)-7x)(5)
thank you so much for doing this!
i can never learn properly in school because my mind wanders a lot, and if i miss even 1 thing the teacher says, i won't understand the entire lesson!
but i can always replay videos and that's the best part
A good teacher makes a world of diference.
Thank you!
Never ever thought I would be smiling after learning Math.... You are math super fun... Loving it and getting confident with every passing video :-)
Id been having trouble with calculus and its all gone after your tutorials. :) Thanks a ton, Sal!
i always use your videos to prepare for tests and exams. thanks for making math so much easier
These calculus videoes are top notch, better than education at universities and paid courses
I know man!!!! I hate that shit, when you get taught something in a simplistic fashion, and they expect you to know what to do when it becomes this complex!!!!!
dude you are the best math teacher ever man.... good job i get this stuff man thanks.!!!
I got a 102% in pre-cal with your help, now its summer time and learning calculus too! Wish me luck on AP Calculus the coming year hehe :)
And helping dreams too..I am back to maths after couple of years of break and here I found my class ! God bless you Sir !
was waiting on that last set of brackets :) Great job as always.
This actually makes a lot more sense. My teacher taught us to go outside-in. This is a lot better in my opinion.
Excellent explanation and I learned a lot, so much that I could catch a mistake, somebody also did before me.
Final answer: [(15x^2-7)(5)(5x^3-7x)^4-6x^-3] (3)[3x^-2+(5x^3-7x)^5]^2
U have a completely different face and life than I imagined when I listened to and watched your videos!
I have no word to thank you becoz I want give you very very very very big thanks.May God Bless You....
This helps me more than my professor. Thankyou sooooo much.
jazakum'ALLAH'UKHAYRIN! may, GOD bless you and I eveyone else watching these videos!
No you didn't confuse us. You r the one of rare best teachers globally. And i really like ur voice and the way you talk. Thanks sir.
Khanacademy saved my life, period.
How is your voice so soothing???
So.. so.. so.....good one of the best e-tutors....!!!!!😀😀😊😊😊🌀
10mins and a chapter worth of doubts are now cleared!
very good, i want to point out just one thing , in the last problem you need to put a parenthesis "or brackets"in [(15x^2-7)(5)(5x^3-7x)^4-6x^-3] so that way it would be [(15x^2-7)(5)(5x^3-7x)^4-6x^-3] (3)[3x^-2+(5x^3-7x)^5]^2
You are a life saver. My lecture is super smart, but you seem to explain it in a more understandable way
Confused me? My teacher confuses me!
This is what teaching should be, taking time to explain the steps. My teacher taught us the chain rule in one class (2 hours). The next day we were given an in class assignment with the chain rule, but with fractions and rationals. In my head, I was saying ''God help me''.
Teaching is an art, and thank god there are still some good teachers out there sharing their knowledge for free. Thank you.
It's about end of 2023 and i hope our dear teacher and all those who commented here are alive and happy 😊
sorry for my english 😅
this is soooo much easier for me to understand...i havn't been getting good grades in calc and i think im finally getting caught up
you're so much better than my current calculus professor, THANK YOU!
2:25 "To the minuuus 8." I don't know why, but something about the way you said that was hilarious. Thank you for making these videos and being awesome.
YOU ARE A MESSIAH..... Of my marks, thank you so much!
Good at explaining with a lack of assumptions, and the mouse writing is clean too
He does that, but in reverse order. Where the brown in the last line is the derivative of the large bracket, the pink times the green accounts for the derivative of the inner portion you mentioned: dy/dx (3x(-2)+(5x(3)-7x)(5). The light blue is the derivative of the last remaining inner portion: dy/dx (5x(3)-7x)(5). I was taught to tackle the outside first, so his method appeared a little backwards to me at first.
This review well for me learning for others is great your sessions are well timed so never to long and easy to follow. I forgot how long these calculus problems can get. If I remember correctly some problems can get extremely long.
Thanks for all your videos! Very helpful in exam period!
im studying egineering and i have no idea what i'd do without these vids...
Sal should make a playlist dedicated to teaching "teachers" to teach.
so to find derivitave of "blob" raised to a power you just pull one "blob" out and find the derivitave of "blob" and then multiply it by the derivitave of what you are left with when you pulled one "blob" out.
Is that right?
Nice tutorial!
It really helped me with my homework :D
Thanks for sharing your knowledge xD
Wow. Your explaination is so short and easy to understand ! thank you
You are explaining 20x better than my teacher . Keep it up good sir ! You're awesome!
i actually followed through the whole problem, thank you.
you didn't confuse us ...you just cleared all our confusions !
Best explaination ....👍👍👍👍
Thanks for all you do Khan Academy
I appreciate the work done and time given in producing these videos but Good God - perhaps we could all chip in a few quid and enable Khan to purchase some more refined writing and video software.
In other words, I suspect that many whom wish to learn Maths pause the video, in order to follow it through and reckon it in their own heads. But its almost impossible to see what is written.
this is from 2007 he prob upgraded
B J is correct. The video is from 2007. Not only was the technology not great at the time, video quality was also not HD.
Omg... I actually got that.... if my University professor had attempted to teach me this then there is no way in hell i would have followed so clearly.
Forever grateful to Sal!
Perfect example . Thanks 👍👍👍👍
wow. amazing. thankyou! my $4000 tuition money for the subject would be better off with you...atleast itd pay off by me actually learning something. thankyou soo much
I love you.....
My god I feel so sorry for the people in the comments here that have teachers who don't explain it this way! My math teacher was excellent and she always made sure to go through everything step by step, even when we had two months less than everyone else to do calc (IB is hard). I'm glad these videos are here for people who aren't lucky enough to have teachers this amazing in school.
Yeah man, you are awsome, thank you for your lessons !!! Thought I can't learn these things :-D, but its quite clear now, you saved me a lot of time...
dude u justify the quote that says " I bunk school to study in peace". thanks man . great help
Khan is brilliant!
You do make maths easier. Thanks Khan.
My savior :'). I was scared, and instead of going to church, I went to Khan Academy.
Very Helpful, thankful !
Thank you so much! Your way of teaching is amazing!
Mistake at 3:00 i think but thank you for teaching me this. Your videos are gonna get me to college!!!
thank you!! my finals on thursday this is very helpful!
Mine is this Thursday. How did you do?
Bryan Frei Rejected
Bryan Frei Rejected
+Mythrunes lol
You're my online study buddy! Yaay!
I hope you got many more examples in stock ;-)
this guy is dangerously good.
does the first chain go on forever? How do you know when to stop? lets say you stop at the answer where the 2nd term is raised to the -8. so, you could keep subtracting one indefinitely?
I want a shirt with Sal's face smiling inside of a heart.
its a really complicated example ! i am wondering if we can find this polynomial equation in real life situation.
I noticed you wrote a ^2 instead of a ^1, you were showing that there is a ^1 but when you copied it down in yellow you mistook it for a 2 :) Thanks for this anyway