ไม่สามารถเล่นวิดีโอนี้
ขออภัยในความไม่สะดวก
Product rule | Taking derivatives | Differential Calculus | Khan Academy
ฝัง
- เผยแพร่เมื่อ 17 ส.ค. 2024
- Watch the next lesson: www.khanacadem...
Missed the previous lesson?
www.khanacadem...
Differential calculus on Khan Academy: Limit introduction, squeeze theorem, and epsilon-delta definition of limits.
About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.
For free. For everyone. Forever. #YouCanLearnAnything
Subscribe to KhanAcademy’s Differential Calculus channel:
/ channel
Subscribe to KhanAcademy: www.youtube.co...
![Exclusive! น้องลิกก้า&น้องโรร่า มาแล้ว!! [cc] แดนแพทตี้ SS2 | EP.48 |](http://i.ytimg.com/vi/UmlpJhRekyY/mqdefault.jpg)
Honestly your making me want to cry. The fact that i can understand a concept so thoroughly from a youtube video, opposed to my professor, is worrying. Thanks a lot whoever is behind this
the man the myth the legend..... Sal Khan
none unknown bruh that was posted 3 years ago
maybe you're not paying as much attention in class then you are in a TH-cam video.
you're*****
Lmao, this comment really was posted when I was 10 years old and in 4th grade, now I’m a few weeks away from graduating high school. And this video... it was posted when I was just three years old.
It's sad that a video from exactly 10 years ago from today (10-3-2017) taught me more in 10 minutes than a 2.5 hour lecture by someone who gets paid to teach it.
They're doing their best. Cut them some slack. It's not fair to compare your teachers (mere mortals) to the almighty maths GoD that we know as Sal.
Closeted Milenial Schizo person dude
“mere mortals”
😂😂😂
@@closetedmilenialschizopers8734 yaa hail sal lol
from year 2020 here
@@sanugabimsara1289 same here
My professors should be sending you a percentage of their paycheck!
HA
13years later you're still saving lives
Yup
I don't know who you are, but you sir, are my hero. I hope you're getting the recognition you deserve for the help you provide students on the daily.
Give this man a Nobel Prize
I have gone back to school (quite a mature student) and am starting my degree next semester, you have made me feel so confident i can do it. Many thanks good sir :D
Funny, my midterm is tomorrow and I'm watching/learning this exactly 10 years after it was uploaded. October 3, 2007 - October 3, 2017.
And here I am in the same boat, another year later xD
And after a month here......
After a year ;)
@@adriancres8598 after a year (:
my midterm is tomorrow!
I'm glad I found this channel... Tomorrow is my maths exam re-test... (Bcz i failed in the first one) and I didn't understand this chapter... Now I've understood it properly
I'm in AP Calc and you, sir, have saved my life, and possibly the lives of everyone I know.
Hats off to you.
I hope no one minds my pointing out, here's a much simpler way to illustrate the product rule, that also reinforces a more basic derivative:
f(x)=x*x
f'(x)=(x*1)+(1*x)
f'(x)=x+x
f'(x)=2x
You ARE right, but that is a short cut. he is showing the actual definition for beginners
I do exactly similar exercises, showing the product rule works on examples where we already know the answer :) It's a great way to see that it actually works!
You are correct in the basics but you missed that the product rule is the simple solution.
It must feel good to see all these positive comments, and you deserve each one. The teaching methodology you employ in your videos is extremely learner-friendly, and lends itself to people who aren't intuitive when it comes to mathematics. Kudos.
This has helped me so much. I have my exam tomorrow and I couldn't understand so many topics because I was basically moping around and my teacher is pathetic but I came her today and BOOM! Thank you so much Khan! Whoever is behind this! ❤️ I want to give a hug to you.
Oh, and for anyone else who reads this, it really helps to go along with a pencil and paper (I use a lap sized whiteboard and dry-erase markers) and solve it as Sal does. I like doing it in lectures, but it works even better with the videos since you can pause it if you need more time (and I find actually doing it to be one of the best ways to remember how to do it later, plus you can absorb Sal's intuition while doing that).
Give this man A Noble prize already. GOAT!
How which category? For what research?
Sal, you're the only one who's doing all the tutorials for all the subjects?
He mainly does the math subject, but he also does some of history, but not all of it. It's a diffrent teacher that does it.
I've learnt more about the chain and product rule in the past 9 minutes than I did in a whole semester
I really don't understand how the hell it's possibly for you to be so understandable, it's almost as if your brain is connected to mine and just feeding the information into digestible chunks. Thanks so much!!!
I totally understand how to do it now! only thing I don't get is how do you simplify it? (currently doing a summer project for calculus & I can't remember much) 😩😭
@DryBones111 Multiply two variables together. When they're adding, you can just derive them separately and add them together after, but when they are multiplied, you have to use this rule.
I learn WAY more from you than I do from my college classes. Thanks
Thanks for the explanation. I'm very happy that there are people out there in the world that can help the struggle.
no, doesn't matter. Order doesn't matter when you multiply.
at 7.17, should it not go from -5 to -6 instead of -4?
I made that exact mistake too, thanks for posting it so I could see Unli Revs's response
@Unli Revs Thanks for posting this clarification
youre amazing, Even though i have a really good calc teacher, i can always supplement the lectures with your videos and it really is making things easier. Thanks you so much
Me watching this in dec 2018.
Thanks a lot to the person behind this, i just don't understand what our teacher teached us but this, its kinda makes me thinks that i actually good at this hahahaha
omg thank you, i always thought he did it too fast and it all went over my head!!
I've seen a lot of people, or teachers, let their ego get in the way when teaching something especially math. They like to make it as complicated as possible so that you will find it more difficult to understand so that they will look smarter. Khan however doesn't do that. He tries to simplify everything so that it is more understandable, which actually makes him look much starter than those aforementioned.
thank you sooooo much. we were "shown" how to do this in class today. my teacher barely explained a thing. this, and your other videos, have helped me so much. again my full THANKS!
This video is as old as me yet more informative than my teachers
Khan what can i say ! i thought i am really bad and i'll never understand this things . but with you it looks very simple and easy ! Thanks a lot .
sorry for my bad English tho
Jesus Christ I never understood a thing in my calc course and this will certainly help my calc quiz tmr! Thanks alot! From 2023 btw
Hello! I'm from Brazil and I'm really glad I've found your video. I could learn in a few hours what was so hard to get from the books. Thanks a lot!!!
yeah that's right (and the same thing as what is in the video)
Awesome! I'm teaching myself calculus with your videos--thanks so much for providing these concise and clear lessons. :-)
We just started derivatives and I had already known the power rule, and the addition and subtraction rules too. I was using the difference quotient on the problems to practice because they were easy problems and just using the other rules to check. I was planning on breaking those out on the test to save time, but then one kid in my class said he found a shortcut (he figured out the power rule) so my teacher said he was taking all of the polynomials off the test. So now I'm learning the other rules so I can ace the test in ten minutes I mean he can't say I'm cheating if I prove the math
I'm pausing the video every time you write an example problem to work it out before you do.
It helps a whole hell of a lot.
I finally learned this stuff properly, thanks so much, i hope you upload more complex examples of chain and product rule as well the Quotient Rule
Dawood Goga I
Khan your great and thank you cuz I finally understand calc but plz continue to talk slow cuz your new videos you talk to fast and its harder to grasp
hey man u deserve a nobel 👍👌👌👏👏
I like how you change the color to be more pleasant :)
for example 2^2 * 2^2 = 16 . you can write it also as 2^2 *2 + 2^2*2 = 2(2^2+2) = 2 *(2^3) = 2^4 = 2^2 * 2^2 = 16 . The product rule .
I got killed in calc 1 because my teacher could not break this stuff down like Khan does. Thanks man. I wish I knew about this channel earlier.
no like i love you..like honestly
From now on, you're my new professor... unlike the other one who's a mean grader. Thanks for the vids!
It's really simple take for instance 2^4 that's 2 time 2 times 2 times 2 so 2,4,8,16 ... 16 if you divide 16 by 2 (8) it should equal 2^3 that's 2 cubed or 2 time 2 times 2... so 2,4,8 which it does!!! so all you do to reduce a power by 1 is divide by the coefficient (that's the number in front of the power) ... using that we can find out
2^4=16 divided by 2
2^3=8 divided by 2
2^2 =4 divided by 2
2^1=2 divided by 2
2^0= following the pattern you see 2^0 = 1 as 2/2 = 1
This is fun👍🏼 thank you
excellent 5 stars excellent :), you're so great at teaching that I actually tell my friends that you're my tutor.
You have pretty much carried me through Math, Biology and Chemistry through year 11 and 12 :P
u(dv/dx) + v(du/dx)
very similar to quotient rule
(v(du/dx)-u(dv/dx))/v^2
Dr. Khan is what I'm gonna call you coz u bring pride and satisfaction to the teaching of the mathematical discipline...PS You are the Bomb + U have a sizable population of FANS in India!
Im in college right now and i just don't go to the class, other than to take the tests so you've got a great idea
You sir just saved my grade in honors calculus, i am forever in your debt
sal you're the man. product = quotient rule saves me much confusion. i'm teaching myself calculus before i take it in the fall and i'm beasting this material so far. thanks so much.
you got it.
Well it's arbitrary now, but when you get more into it you'll see that the dy/dx makes a lot of sense.
omG I struggled so much with this in class today but after watching your videos, it is sooooooo easy!
awesome I have improved a lot just because of ur videos thank u!!!
Think7 as 7x^0 (any thing to the power of zero is one) times the number in front of x by the power (7 times 0) equals 0 take one off the power and you get 0x^-1 which is 0 divided by x which is zero (or you can just think anything times 0 is 0 so 0 times x^-1 must be 0)
The reson anything to the power of zero is one is because you have to divided the number by itself to get to zero... e.g. 2^3 (8) divided by 2 is 2^2 (4) divided by 2 is 2^1 ( two) divided by 2 is 2^0 (or 2 divided by 2 is 1)
I'm a student at CU Boulder and I think you just saved my calculus grade.
Making up ad hoc examples produces unique results. Guess is no easy way to make this more interesting for people.
Just watch his playlists on whatever course you plan on taking, test on it (Clept) and opt out of it. Save money, graduate faster, learn more.
YOU are a friend to the WORLD!
@ChemaShima No, he has it correctly. The original in equation is 3x^ -3 and not 3x^ -5.
I'm in college, and I'm already doing this. It works!
@TheFashionvictim6 I think I messed up, it should be -324. It's dy/dx= (1-x^2)^3. So the outside power goes in front and you subtract 1 from the power... 3-1 = 2. So we have... dy/dx= 3(1-x^2)^2. That's the first part. We then have to multiply by the derivative of the inside. So we then have dy/dx = 3(1-x^2)^2•(-2x).
Plug in x = 2 you should get
-324 it's 2:00am so...yeah. Hope this helps!!
its the quotient rule video. you can find all the videos in the calculus playlist :)
first i watched this video when i was in high school and now i am watching this in my computer science degree for revision to do artificial intelligence
On last one. When you took 1 away from -5 how did you get -4. Wouldnt that be -6 or is there something im missing. That got me confuses but awesome video
I do it in the reverse order of you - I find it simpler. I posted it in the last video. I go from out function to inner function. Thinking about it like a tree, it allows me to go from the single branch to the other branches one-by-one. I find that makes complicated instances of the chain rule much easier since the structure naturally sorts itself out without my figuring out what term goes where (I posted an example in the last video).
Thanks for the videos Sal, this is still good review!
Great video, I like that you used high positive and negative powers for variables. I believe it exposes students to problems that they would not be too frightened of, especially when a test/exam comes up.
I love you
You saved my life😍😍😍😍
Why didn't I find these videos months ago? They help so much!
1. Use the definition of the derivative to calculate the derivative f′(x) of f(x) := x + c, where c is a
constant. Using this, and the product rule, differentiate the function g given by
g(x) := (x + 1)(x + 2).
Check your answer by expanding the formula for g(x) and then differentiating.
How would you do this? lol
Wow! These lessons make so much sense! Thank you so much!
this guy make it so simple
This guy is a freaking genius! I wonder if he does private tutoring
For those that want some more practice, I just uploaded a video where I solve such exercises step-by-step, perhaps that might help :)
THANK YOU! dy/dx always confused me, although I knew there was something like that I couldn't be sure... now I know:
f'(x) = dy/dx = (something arbitrary)!
last 1 blow my mind
You sir, are a life saver.
@TheFashionvictim6 I believe the answer is 48. dy/dx = 3(-2x)^2. Then you said x = 2, so...substitute -- 3(-2(2))^2 = 48.
I’m pretty sure that’s orange not brown bud
@ChemaShima no even though it looks like 3x^-5 it's actually 3x^-3
these videos are so good that they don't even need to be above 240p
Now I want to know what that last function looks like.
I'm a little confused. You have the product rule as f'(x)=h'(x)g(x) + h(x)g'(x). For the problem f(x)=(5x^5-x^7)(20x^2+3x^-7), when we go to plug stuff into the formula, for the part "+h(x)g'(x)", why do you have it as (40x-21x^-8)(5x^5-x^7) and not the other way around? I thought g'(x)=40x-21x^-8 and h(x)=5x^5-x^7. Or am I over thinking this and the order doesn't matter? Orrr am I just wrong overall, which could possibly be an option..
thank you for this, I get lost with the problems similar to the last one
thank you for your fully explain to me! i didn't pass before, when i watch your videos i got pass !!! thanks so much :D
thanks sir for making me understand the chain rule
Here I am fretting and hyperventilating and after watching you explain it everything clicked. Thank you
Sal ur the real MVP !!!
ur videoes help me understand theses concepts in such a good manner.....thank you
Es la calma de la arena
Golpeada por el mar
Esa calma que hay en todos
Frágil como un cristal
Que nos dice y que nos cuenta
Que el amor traerá... calma
what happens when f(x)=g(x)*k(x)*h(x) for example? how will the product rule be apllied here? And what happens if f(x) has four factors like : f(x)=g(x)*k(x)*h(x)*t(x)?
Thank you so much, you are the best sir
cheers, question does it matter which equation comes first?? V THEN U or U THEN V
Wooow ' you have 3 million follows i ma really happy for you 👏👏👏👏🌷
Thank you i can understand now 🤜🤛
I find it so annoying that I cant understand in class but understand a video so much easier
I have a question guys and I need an answer ASAP pls. Why can't we just simplify first the 2 equations (by distributive property) so that it will become a polinomial and easier for us to differentiate?
This is a major issue that he can teach in 8 minutes what it takes professors a whole unit to teach.
I love it when he says: "This will optimally confuse you" xD...