Calculus: Derivatives 2 | Taking derivatives | Differential Calculus | Khan Academy
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- Опубліковано 9 лют 2025
- More intuition of what a derivative is. Using the derivative to find the slope at any point along f(x)=x^2
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Differential calculus on Khan Academy: Limit introduction, squeeze theorem, and epsilon-delta definition of limits.
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Thanks for catching that. My brain sometimes malfunctions while doing these videos. Actually, I had a back injury the day before so I'll just blame it on that :)
-Sal
you got it right but we are in a limbo 6+ h left stand alone what to do with that Slope is 6+h and what is the h? Khan do it again
4:30 it will be 6+h.. Not 6+h^2
Khan Academy 👍
i love all your video i am structural engineer and everyday i keep watching your video sinc i was18 years old thanks alot man ...god bless you
awe thank you for the video though! :>
I watched a 30 min video for my college calc class, they never gave a definition of a derivative, watch an 11-year-old Khan Acadamy 9 min video get all the answers I need. Thank you!
Isn't it 6+h if you factor and simplify that expression?
Yes
i agree
dani gómez yes but it doesn't really matter in this case because h is going to be 0 either way
Yeah I caught that too and immediately went down to the comments LOL
Zagros Hama not in this case.....
that's right. My brains breaks down every couple of videos
Khan Academy Still you rock!
You're still awesome Sal!
You are soooo... helpful, thank you!
This guy gives free education to the world, no one bats an eye. He makes a mistake and everyone goes crazy...smh
Khurram Solangi well said boy! I absolutely agree
He actually makes mistakes all the time. On his website he has annotations correcting them.
bruh this man big scholar fham. if he make mistake obv we help the brother out like wdym.
mistakes happen. That's ok.
True, I noticed it as well but I'm not going to say anything because I saw about 6 comments about the mistake. If you can notice iy, good for you finish the problem the right way. Humans make mistake.
OHHH I wish all teachers be like him, clear and on the point.
this guy needs to teach everyone and get rid of all high school teachers and college teachers
Su Sang I don't know.... he can't even simplify (6h+h^2)/h
Plus, the answer would still be 6 even if he didn't make the mistake.
but I like my math teacher
Motivational video
this man taught me quantum physics in 6th grade !
7:07-7:09 I have never heard Sal so furious before.
The joke is that he never gets angry, and that the little frustration in his voice is the closest we will ever see to him expressing anger.
Ur mom
Sal? I like his voice, so calming
never have i seen a person laughs when hes furious, haha.
If this was taught this way at every high school, we'd have a lot more mathematicians & physicists @ the universities. Keep up the good work ;)
Saving lives 17+ years on! Please keep it free!!
YOUUU are saving me from SOO many emotional breakdowns!
No one replied to you for 8 years, so i am doing that,
@@g-code9821 No replied to you for 3 months so ill do that :)
@@jaywankhede3426 No one replied for you in 1 week, so ill do that :)
@Mohammad Pourheydarian No one has replied in 2 weeks so I’m doing that :)
@@ghastiafy67 No one replied to you for 1 month, so I am doing that.
This was explained better than the 2 days of 1 hour 20 min classes that my teacher was trying to teach us. I am soo glad that I found this. I was soo lost and this really really made it easier to understand.
The unit of the slope is the unit of the y per the unit of the x. So if the y axis is meters and the x axis is secods, the unit of the slope would meters/sec or velocity.
GOT IT ! Thankssss
Im in 6th grade trying to learn derivatives. I literally love you. You helped me so much. I thought it was impossible but after this video, it seems like basic math. Thanks a lot
There's just something about your L's when you draw the abbreviation "lim" that's just so satisfying.
Awesome work though :)
I believe ‘cursive’ is the word you’re looking for mate. Lol.
I do the power rule later. The derivative rules were all derived using limits. I want to do it this way to show where things like the power rule came from.
im in 7th grade trying to learn physics on my own at home- you guys really help you have no idea how much youve helped me at self teaching and at school
aye man what are you doing now i am in 9th and doing the same
It should be 6+h, either way it has same answer =6...thanks for the tutorial sir! Keep up the good work
Where did the 6 come from on minute 3:07?
@@faridsierra726 If you expand the grouped term(3+h)^2 it will be 9 + 6h + h^2
@@humanityline2023 I just remembered how these things work since it's squared💀 Thank you so much
"Well what does this tell us ? What have we done for ourselves ?" Lol
bernie Mahoney I died. 😂😂😂😂
lmao so true
Kudos to you good sir! I'm working on a project for our pre calculus, and I've been stuck on a problem very similar to this for already a week. Glad you're alive and teaching math. Keep on rocking math 🤘
No matter what year it is. These videos will get views. We all need math help
He makes it look so easy
thanks to him, tho
Minute of silent for those who didn't finish past part 1
If you take the arctan of the slope you get the degree of inclination/declination
you were correct it was Lagrange
dauummnnnn...this is soo sikk..i just started calculus and i already know whts going on. thank you soo much!!
Thank you no one has been able to teach me derivatives. I’m in 8th grade somewhere in between Algebra 1 and 2, but I can still understand the process and take away useful information from this video. Calculus is awesome, can’t wait to learn more about it with your helpful videos!
Superbly simplified. Thanks a lot for that video!
And thank you also for highlighting the error - which anyone of us can make - to stop people from pointing it out over and over again ...
Holy crap.
I've always been pretty okay in class, but due to personal reasons I had to miss many days of Calculus when I was learning it back in high school. When I came back, the teacher had already went over derivatives fully. I asked him whether he could help me/teach me, but he said no(my school was an all boys one, so it wasn't common for teachers to act "tough" even if they wanted to help). As such, I eventually came to understand derivatives and how to figure out the derivative of an equation, but never as well as I would have liked.
I'm fully graduated out of college and I'm starting work as a software engineer. On a whim, I thought I should relearn derivatives once and for all--properly this time, directly from Sal Khan.
Holy crap--I am not exaggerating when I say I had to pause the video multiple times as I felt euphoria over getting concepts I had mostly just memorized for years. I never learned the definition of a derivative in terms of that limit--NEVER. Maybe my classmates did, but I had to guess lol. My jaw dropped when you reduced the limit to f'(x)=2x. I knew that x^2 would be derived into 2x--I never knew why. You've literally opened by eyes not just exactly *what* a derivative is(which I sort of knew before), or how to take a derivative(I memorized a ton of equations for my AP Calc test), but *HOW* it actually works. Thank you Sal, I don't know if you'll see this but you've truly made the transfer of valuable knowledge more efficient for everyone around the world.
Kimchi, I had the same problem ... I missed these derivatives classes, and never could understand thoroughly ... until today ... 👍👍👍
Mr.Khan, u explained something to me in 9 minutes that my uni teacher couldnt in 5 weeks. thank you
Omg the effort you put in these videos is unbelievable sir. Thank you so much❤ I really hope you are doing good in these tuff days❣
I got it right before he said the answer.. I've never been more proud. 😂😂
Lol
Thank you was lost and now found!! Many year middle school teacher - first time calc student!!! Have a calc for teachers class and felt totally stupid - like I should get this fast!!! But the high school teachers make the pace so fast!! Thank you for helping me understand this!
You are an amazing math teacher - going to lectures and going over my notes didnt help as much as you!
Dude, that is sick. I'm in Mechanical Engineering and I had no idea I could do things like this. I used to just memorize these things.
ur an engineer and you didn't know this?
i’ve been struggling w these equations for about a week now and after watching this i solved a problem in about two minutes
"Ahhh.. I need to get another tool..." :D
you are awesome! Your vids are really helpful!
Lol I'm a Finnish ninth grader and I actually understand this. Pretty well done mate! :)
People like you are real god. For all those who mind his mistakes so seriously, it's not that God never makes mistakes.
I skipped every lecture, showed up to the midterm and final and aced the class partly because of you, kind sir!
These few derivative video's have helped me in 20 minutes as much as 5 weeks of class. Thank you.
I'm thirteen and I was able to keep up with you as you walked me through it. Wow, you're amazing! Subscribed.
And now you're 22, wonder how your life's been going for these past 9 years. Went to college? Married?
That is assuming you'll miraculously get a notification about this reply.
I understand this, I'm 14 you the best teacher ever in maths and other stuff I've watched
You are indeed the Bob Ross of Calculus!!!! Good job on the explanation super simple.
lets derive some happy little slopes
This comment is so true!
i was17,i finally know about the d/dx x^3 = x3x^2
n(x^n-1)
and how the d law come from:[f(x+h)-f(x)] / [x+h-x}].
i aim physics and math throughout my study.
i think science is the best,and thank alot!
you are amazing teacher. the way you broke this down is good work
same here. I'm 14 and this makes perfect sense.
Thank you, Khan! You never fail me when my professors consistently fail me over and over in class. From economics to science to math, you're always there to make me understand things way easier then the bull crap professors do on the board. Thanks again, dude!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
sir u should be my teacher for this class.. u make more sense than my proff.. at school... thanks
explains everything I never learned at class :D
you really made me understand this concept
I've been watching a million videos on this but this one helped the most. Thank you so much!!
Regardless of the mistake, this video is a blessing.
This guy is the real mvp
oh those are really easy to understand
When I get my first salary, a portion of it's gotta go to khan academy.
Saved me for my derivative test XD thank you
You are better than my teacher, hope I learn in time to pass the ramaining tests and pass the semester
That's help me a lot to understood calculus limitation
this video is really helping me here in 2020...the future ofcourse
I never thought i'd say that i liked any part of calculus. this is pretty neat.
Alternate title: Sal complains about his pen for 9 minutes straight.
This is a big help to me..
i gots an exam in an hour. YOU ARE MY HERO.
wow, this is great! i'm studying in germany right now, and they have been recently critized for their poor teaching skills in science and math, which is totally true! plus the fact that i am attempting to learn calculus after not even being done with algebra and also having it in another language... AHHH. but now i think i'll be able to pass my test tomorrow!
thanks!
dude thanks so much youtube makes learning so funner than in school for some reason
Thank you so much, do not worry about the h^2, most people at this level understand that it was the frozen pen/CPU getting in your way, Nice video......
The rule when expanding a quadratic is for (x+h)^2 is, x^2 + 2(x*h) + h^2
God fucking bless you !! What a time to be alive!
Your explanation is way more clear than my professor
;(
I remember using that long equation senior year of high school, a month lather the teacher showed us a way easier way to find derivatives
Pls tell me howwww
Yoo Youngjae
n*ax^(n-1)
Use this for every ax^n
Yoo Youngjae
Example
X^2
2x
Example
3x^6
18x^5
yeah, I was wondering if I'd totally forgotten how to simplify...but I was glad still haven't (nearly 12 years later). Thanks for the explanation it was very clear.
Thank you Sir😭😭 i was so confused but you helped me understand, thank you
Well, that was much simpler than what I was expecting... thanks!
right on, same here.
Well, H is just some generic variable he applied to denote that some generic change to x happened to make f(x+h). Applying the slope formula to that gives you the slope of the secant (passes through two points) line. You don't want the secant line slope, though, because that's an approximation. You want the slope as h (that generic variable) approaches 0, which will give us the slope at exactly whatever that point is.
Calculus is indeed tough, i want to learn advanced statistics and this is used.
What he did was the FOIL method of expanding the squared expression (3+h)^2.
The quantity is 3+h, and that quantity squared is written as (3+h)(3+h). You can use the FOIL method to expand this and get 3*3+3h+h3+hh. Simplify this to get 9+6h+h^2.
I hope this answers your question. If you are unfamiliar with FOILing, I suggest finding a video like this one that details it. Khan probably has one about it, too, he covers virtually everything!
That's some of the most basic algebra there is. I seriously doubt anyone not familiar with it would have any reason to check out videos on derivatives.
thanks for this comment, i'm a total math noob and was trying to deduce simplifications by hand and that didn't make any sense, but I thought, ok, one of those math rules you don't understand because it's built over a thousand math principles you don't know ! got the notion it was a mistake when he got to the part of 2x+h simplification coming from 2xh + sqr(h). This is a great video.
Man, thank you from the bottom of my heart! It all looks so easy when I watch it this way...
I can confirm that this is still helpful in 2020! Thanks!
After 7 three hour lectures I was more confused than when I started. Watched first 2 derivative vids and it makes sense.
Love the sloppy graphs...look exactly like my chicken scratches!
I have already emailed some classmates to check your vids out ! Thanks
Yeah. You've got it.
Thank you it was great 💛 .
you explain it better than my calculus professor he didnt even give us the graphing approach to the problem before diving into all the algebra
wtf
There is a simplier way to solve this equation:
Coeffient*exponent^ exponent - 1
for the first problem x^2 u will get 2x ( because coeffient 1* eponent 2= 2 and for the exponent value 2-1 =1 or x raised to the first)
from there plug in the x value of 3 in the derivative (2x) and the answer is 6
U helped somehow thanks
great job on the vids. I finally just now understand the definition of a derivative.. even tho my class is on derivatives of logarithms.. ps.. I saw a different guy just use paper and a permanent marker..... much less 'cpu-intensive'
well done to you, unfortunately not everybody had such a perfect education.
I'm only in trig right now and won't be taking calc till next fall, but I fully understand this stuff! Thanks a lot!!
30. f(x)=(x-2)^2 - lambda(x+1)(x+2)
Find the values of lambda such that the equation f(x)= 0 has two equal roots. Show that when lambda = 2, f(x) has a maximum value of 25.
After 12 years this video still helping😘
very nice explanation
When you "cancel out", remember you are cancelling factors. It can't be done with addition or subtraction, which is exactly what the second part of your calculation shows. Changing the operation from multiplication to addition changes what tricks we can use to simply problems (like cancelling out).
Let me adjust your example for a different perspective: what if h=? and 5h/5
- Looking at 5h, we see 2 factors: 5 and h.
- If we "cancel out" the 5's, we're left with 1h/1, or simply h.
Thx alot ❤️❤️
Good job.
I love this ❤❤❤
This is a somewhat belated reply, but it might still be useful.
The problem is probably that the functions are working with radians, while you are inputting degrees, or vise-versa.
This both hurts my head, and is extremely awesome!
Thank you, Khan!
apply (a+b) hold square formula