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Power rule introduction (old) | Taking derivatives | Differential Calculus | Khan Academy
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- เผยแพร่เมื่อ 2 ต.ค. 2007
- Determining the derivatives of simple polynomials.
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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.
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It's been 8 years and almost 10 months since this video was made... I sincerely hope he's gotten a new pen by now.
He already did. Give it another 8 years and you'll probably be watching Khan Academy in 3D.
+The Family Picture lol
***** You just wait. You'll feel like you can just reach out and touch the polynomials with your fingertip!
lol that's good !
He already got a new pen and everything looks clearer now, I try to avoid his videos with the old pen and try to look for another one about that same topic
Whenever I watch Khanacademy's videos, I feel like the entire universe just makes total sense all of a sudden.
How is it going 8 years later
@@dularar8934 If she was learning this in high school as a freshman (where most people do) she probably has graduated with a master's degree.
@@78anurag freshman in hs taking calculus i or AB, no way.
This is one of the best things to come from the internet (imho) - an altruistic push towards free, quality education available to anyone. Not only that, but the teaching methodology improves over time, so the learnability and retention of material can improve for students of all backgrounds! Loved Sal's TEDTalk on AI and Education, he's a true pioneer.
Better than any textbook and probably most professors that try and teach this subject. Thank you for all that you do!
You needed better textbooks man, try RD dharma Class 11 or HC verma vol 1
Learned more from this than my entire semester so far.
Mrraaaaggghhh!
Very worrying if this is true. What on earth goes on where you are studying, do you or any teachers do any work there?
It was a russian who could not be understood. I was exaggerating also
Cal is easy, it's all good. (One year later)
Merica how about now
God bless the guy who invented the internet. 😆
Here I am in the middle of the Australian bush learning calculus.
Tim berners lee, invented the internet.
This is one of the best channels on TH-cam and I feel so sorry for fellow students who haven't come across it yet. You've made me fall in love with calculus. Thank you
Someone buy this helpful man a bamboo drawing board so he can write in peace.
My teacher looks useless next to this, I would like to thank you for saving my university place for September...I was about to fail calculus. I could not understand a thing, until now.
Thanks so much!
This semester was my hardest math class I'd felt in my life, but after I watched this video!!! You're awesome Salman, You helped me a lot.
You sound so happy throughout all of these videos.
Listening to you talking sounds like, "And let's say :D :D x is equal to :D :D :D 4 and :D ..."
Not sure why everyone's guffawing over the "I'm 15 years old" comment. It's not hard to watch a video on TH-cam when you're 15. As long as you're not intimidated by the idea of calculus, learning it from Khanacademy isn't any harder than learning arithmetic when you were little. The fear is what kills most people.
but im 9 years. old
Never thought I'd think this, but calculus is fun. (*_*).
It Sure is!!
This man is a legend he is saving me from failing my calc quiz 12 years later :)
Thank you so much for helping me in conceptualising things. You do save me a lot of time. Thanks!!
I also want to once again thank Sal, and all the people that make these videos possible. Most of us realize he was the driving force, but other people have contributed aswell. These videos helped me through my precalc course to end with a high B after coming in way behind not knowing alot about algebra. They are now helping me learn physics and the calculus behind the calculations for the equations. Thanks again guys/girls, and special thanks to you sal, for being such a great teacher.
This makes so much more sense than what my teacher taught me 🙏🏼
Sal, you're a genius. Why can't everyone explain as well as you do? Whenever I'm stuck in my mathbook, I look at your vids and it's just crystal clear. Thank you :)
I'm just trying to learn ahead, but I gotta say this: You are amazing. Keep up the good work.
So many comments of thanks, but I feel the need to add mine as well.
Many thanks for taking your time to spread free education, especially on such a vast scale. It is truly a marking point in the evolution of man when learning becomes viral. It truly marks a point in the evolution of man, as we approach perfection. What an honor Mr Khan.
He never gets a new pen tool, does he?
Something seriously wrong with his computer and software. He needs to get it sorted before recording any more videos. It is like a broken record, oh my pen stopped working again, blah blah,,,, come on now, you've got an MS in Engineering after all. What a joke!
discuss21
You really don't know who he has become since,eh? Check out khanacademy.com
Kyle Marrotte It was uploaded in 2007.
+discuss21
Just because he has a degree in Engineering it doesn't mean that he wants to stop the video and fix his pen tool.
Also, he might hope that it will eventually stop malfunctioning.
In my class we did the same thing but my teacher explained it different. He never explained why
He said " We have 4x^5 multiply by the power (5)(4x^5) and reduce power by one (5)(4x^5-1) which is 20x^4"
You explain it as "4x^5 = 4 (dy÷dx x^5) = 4 (5x^4) = 20x^4"
Your way is so much easier to understand!
...my teacher just needs to keep his mouth shut and show these videos during class..., the man whispers and talks fast....which is why I have to learn from youtube, these videos are a life saver
Got my IB Math exam tmr... ive been going through almost all calculus videos now. Ive learned more from this guy on a few hours than 1 year of my teachers teaching..
Screw paying a tutor when there are so many better ones online for free...and most of them make perfect sense and more than my teachers! Thanx for the videos
Students : 1
Guy calling on the cell phone : 0
This guy should be everyone's teacher, because the learning is supreme to any other :D
Even for me who doesnt have english as a main language!
"This pen drives me nuts..."
I am SO HAPPY that you help me every day understand math concepts that my proffessor tries to explain... I would fail my semester without your videos.
dude u rock man keep up the gud work u really doing something dat is very moral. i m in school n i m gonna a give a IIT(really tough all india engineering exam) for which my tutions r charging about half a million Rs so wat u r doin is really helping a lot of ppl who r not dat privileged keep it up
Thank you, thank you, thank you so much, your videos had been such a great help! Thank you!!!❤️❤️❤️
Now, whenever I'll study Derivatives I'll think about the malfunctioning pen which drove Sal crazy
Greatest teaching quote ever: "the more examples we do, the better."
Math is FINALLY starting to make some sense!
I was bewildered and feared I might fail my Applied Calculus class but since I found your excellent tutorial videos, I am confident I can beat and be one of the 5 scoring students in the class!! And indeed, I wholeheartedly thank you Salman. May Allah bless you with Janatul Fardowsa*
Most helpful, enthusiastic and optimistic teacher I've seen. I 'Like' Sal's videos at the beginning. There's a 100% chance that the video will be helpful. :)
salman, this is gr8... I wish we had better teachers in school..I had to rote learn all the formulae..
this is way better than my teacher, wow....cant thank you enough
you're sooo much better than my teacher! i didn't know what i was doing until i watched your videos! muchos gracias!!
Thumbs up for this guy helping us in college!
you are a lifesaver! I wish all teachers were capable of teaching like this
Feels so great to unlearn and relearn calculus now after so long (may be 14yrs) :D
you calculus videos helped me gain a better understanding of the topic. i seriously can't thank you enough for what you are doing for those such as myself who need help.
U DESERVE THE NOBLE PRIZE MORE THAN MR OBAMA. I MEAN LOOK AT THIS GUY HE IS TEACHING SOMEONE IN AMERICA, ME IN MIDDLE EAST AND GOD KNOWS WHERE IS THE OTHER ONE. I JUST WANT TO SAY A BIG THANK YOU
omg u made derivatives fun
Thank you so much... I have a terrible time in school... between ADD, and just a simple lack of desire to learn, I rarely walk away from a course learning anything. However, out of the 30 minute's I've spent watching your videos, I've learned more than this entire semester of college.
Wow, watching these videos made calculus sound 100 times easier. Thanks.
That's the point of the derivation: we are searching the slope of a curse at a specific point, which will be equal to the slope of the *tangent* of the curve at that point.
A tangent is a straight line that touches a curve at one and only one point; if you put a (perfect) ball on a table, you can say that the table is tangent to the ball. Calculating the derivative is like putting a ruler on curve and detmining that the slope of the curve at the point of contact = slope of the ruler.
Cool?
oh my gosh this video was uploaded when I was supposed to be learning this in high school. Now I'm learning it and I'm 30 trying to get back into college
omg! thank you thank you thank you! finally...someone just being plain about it! geez!
dude ur pretty good i like ur style and teaching method. pretty awesome im understanding this better. im from sydney australia and pretty impressed with your work. this is helping me get me into shape for me to understand some complex economic theories.
fighting a massive headache and studying for calc exam tomorrow, these are coming in massively handy. (Thank you) ^ ∞
Let's be honest. Raising funds at tutors like Khan Academy and Organic Chemistry Tutor are more helpful to us than buying textbooks at this point.
@WarmBread123 ..basically means 'differentiate with respect to x' (since you're only dealing with x then it's just telling you to take the derivative).... soon you might see dy/dx..and that's 'differentiate y with respect to x'
This guy is easier to understand than reading "The Manga Guide to Calculus".
Somebody get this honorable man a good pen
im sure that he has one now that it has been 15 years lol
OH MY GOD!!!! THIS HAS BEEN LIKE A WEEK LONG SUMMER PROJECT!!!
ALL I WANTED TO DO WAS KNOW HOW PPL FIRST CALCULATED PI AND NOW I'M ADDICTED TO KRACKACADEMY!!!
help me :O
I like the dy/dx notation because it really means 'change in y divided by change in x', so in a real world problem, when you know the change in x, you can then find the change in y (or visa versa); in other words if you're given a change in x, you can calculate the change in y, just by taking the derivative of the function and multiplying it by the change in x (algebraically). Am i making sense? Great videos, Sal! You're awesome!
thank u , u are such an inspirational teacher, now because of you i found out that this stuff is easyyyyyyy, thx :)))
its been 15 years since this video was made, I don't know what ill do if he still hasn't gotten a new pen
Its crucial to master the arithmetics of derivatives.
Thank so much for bringing us this great tutorial !
I guess, 14 years ago it was a big deal to even have the technology to manually write on a device.
Nice video which help me a lot.
I just spent 2h learning derivatives from scratch and the next video in my recommended is "10 signs you might have adhd". Feeling a bit called out rn.
Thanks man I Skipped my homework to watch your videos
he has more videos that can give you real practice.
Very helpful for self-studying calculus! I'll cover the stuff in spivak and in another textbook I found for a dollar, go over problems in each, and refer to these videos to round out that comprehensive study! Thanks!
@TiredNReclasMusic
no the derivitave of 5x would be 5 because 5x^1 so 1 * 5 = 5 so thats the new co-effecient, and the exponent would be suptracted to it would be to the power 0 but thats only to the x. so it would be 5* x^0 = 5*1 = 5.
im in grade 12 and this will help me alot this year. Thankyou very much!!!
x^3 = 3x^2 because you do the power times the constant so 3*x = 3x and then the power you just used which is 3 us decriment it by -1 so 3-1=2 then 2 becomes the new power so final answer is 3x^2
Who is watching this in 2021 and wanna prepare for jee
the main point is, you learn something better than school.
no matter what is behind this.
Only if I could have you as my professor. My day will be a lot more easier and less stressful!
Okay so known that as H approaches zero it equals f(x)+h-x (squared) divided by h. So then (x+h)(squared)-x (squared) divided by h= The limit as H approches zero which equals 0. So next if you take all that info you can see that is x (squared) +2xh+h (squared) -x (squared) divided by h so simplified it would be (2x+h)= 2x which is the formula for f'(x)=2x :)
you're amazing! thank you so much for all you do!
Incredible... Smile all over my face!
Not necessarily, calculus doesn't come into the curriculum here in the UK at all until AS-level in 6th form. (age ~16-18)
Simply fantastic, thank you
very good absolutely useful too bad i couldnt find this three weeks ago lol hopefully you have something on partial derivatives thats what we are on now in class
Derivative of constant can be simply explained like CONSTANT=CONSTANT*X^0=0*X^-1=0...
Sal, you are a beast. :) I am planning on majoring in math and i was wondering what are some of the hardest math courses in college? Congrats for everything you do. Note: if i were a billionaire, i'd donate millions of millions to your academy and you since you quit your job in 09 :)
easy way to know the derivative of simple functions like that are: n X ^n-1 where "n" is the variable of X
I know how to do all the mathematics I just wanted to understand what it means in the real world. fyi you don't have to use the chain rule to solve that problem(if its even applicable) you can just take the derivative of the derivative. Chain rule is use in problems like cos(x^2) where you have multiple components at work.
same thing here- I actually got a natural high and a good mood for the entire day, since I remember seeing all of this "matrix text" in class and here I'm all like "I know kung fu!"
awesome my friend...all of us....really enjoy your videos...from lima peru
The chain rule video explains what to do in that case.
Namely, if f(x) = x^3/3, f'(x) = 3x^2 / 3 so x^2
Not sure, though, I just watched the video, I never practiced the thing.
It's more efficient to watch this 10 minute video rather than listening to my math teacher for 60 minutes a day..
You can find a derivative by multiplying the coefficient by the exponent, then subtracting 1 from the exponent. For example, 6x^4 would be 24x^3. Idk if that helps anyone.
classes aren't going to let you use that polynomial derivative shortcut.. was hoping i could get real prac! :)
You are a skilled teacher! This has made my class much more understandable, I prefer you to my professor :p
These videos are AMAZING! Khan Academy is a blessing!
he makes this fun.
This is the best academy ever! Ever!
tysm man saving lives.
I love you for this video
It's 16 year now. 🎉🎉🎉
@iamtheplauge That happens a lot in my class. At least with computers and online videos you can go back and correct mistakes...
I'm studying slightly ahead, because your videos are so fluid. thank you.
Yeah me too
I am 9th grade so yeah guess I am ahead
Thanks for the excellent teaching. These videos are crystal clear, and very easy to understand.
screw reading my textbook. i'll just watch these videos. much thanks :)
From my understanding you said that the derivative is the slope of a point in a function on a graph is equal to the slope of a tangent line that passes through that point. What if your dealing with a function where the derivative is x^2. How can that be the slope if its not a straight line? I'm sorry if this doesn't make much sense I'm very confused.