Derivative as slope of a tangent line | Taking derivatives | Differential Calculus | Khan Academy

[@kategard6788]

Mr Khan, has anyone ever told you...you the man?

[@maris6843]

One of the best explained videos on how we get to finding the slope of a tangent line. Now the formula we use makes so much sense as well. When I'm learning math it really helps me to know the why of something, versus I know a lot of people are just okay with that's how it is and never question any further. That's not me.

[@jriver64]

Believe it or not, you're the only individual on this earth made it possible for me to understand this section of Calculus. In fact, you have a gift of lecturing on this subject matter with complete ease of simple demonstration. Thank you.

[@merc5333]

Khan Academy I just wanna say that in the first four minutes alone, I have learned and understood what a slope is from this video!! More than I did last year from the tutor and learning program! I have math avoidance (among other things) and I FINALLY can understand the concept of a slope! I'm grateful for that. So, thank you Khan Academy.

[@reindeerman214]

Holy shit math makes more sense in English than in Swedish:/.

[@ruguoserliegise2716]

reindeerman214 lOL

[@dancetron1]

(Not) he said a bunch in this video. After looking that up its simply a short hand for notation in case anyone was wondering the same thing I had.

[@TeodoraMateeva]

Sal's videos are like enlightnment coming from the cosmos and shining through my brain :D

[@0Delluxe]

I don’t usually comment on videos, but honestly sir, you explained the basic idea that we have learned in previous years and then you introduced the new idea based on the previous idea so that we can understand and creat connections regarding that previous idea, and you explained everything so simple yet full of understanding and main points of the topic, You explained the basic idea of slope 1) slope of straight line Then converted that idea to apply it to slope of curve line which include A) slope of curve line -That can be found by taking to points that are very close together,and -drawing a line crossing both points (forming s secant, which is a line that crosses two point in a cruve) - then found slope using those two points (since to find a slope we only need 2 points and apply [change of y] over [change of x] And then you went on and connected the idea of limit to slope Also connected the idea of derivative to slope

[@abbasmawash457]

Ive been in school for 12 years and never realized the meaning of the slope of tangent to the curve Thank you very much

[@jrcr1993]

Oh my god, you taught in 15 min what my math teacher taught me in a week. You're so helpful..Thanks to you i can understand derivatives once for all. thanks!

[@giorgio1apple]

Seems so weird in college but with these videos these subjects seem to be easy enough for kids to learn.

[@SamraiCast]

George Alegre yup pretty much, just need some help with background stuff like derivatives of double-angle formulae 😂

[@nicholasjones5995]

The power of a good teacher who can offer a clear and concise explanation.

[@DanielShively]

im 14 and im learning these things

[@ventingmachine101]

@@DanielShively same

[@codeouter]

9

[@S2DEliptiK]

you just have a flawless way of teaching things

[@REXPATEL1]

I do not know how to thank you enough for this. I have learn calculus from watching your videos, my professor is a big d-bag who only does examples out of the text book, and skips some steps along the way. Here i can understand everything as we move ahead. Thank you So much.

[@LF-js9gx]

Amazing!!!! Must say!!! Two teachers taught this but none explained why we say that this derivative is the line of tangent and y we need to take h approaches 0...truly commendable!!! Keep up the good work👍👍👍👏👏

[@katanphetamine]

fantastic. My professor took over an hour to explain this, and just when I thought I had more or less got it I watch this video and now it's to the T. It's a lot easier to remember rules when you know how they were obtained.

[@suprdbgt23]

Thank you very much. I finally got this concept through my head.

[@crusifixa]

good! , My father is a Mathematician, I ask him to help me with this with no succes... and I remembered the Khan academy !! now I get it!

[@bashfulbrother]

You are really a good instructor. I took all of the math classes in college I could get my hands on, and I did fairly well, but by your manner of dissecting the variables you have cleared something up for me that has puzzled me for a long time. Thanks.

[@dogmanshark]

Math is becoming very useful these days, and now you make it easier to perceive for everybody. Thanks Khan.

[@khalidsayedabdullasayedmoh3795]

Still useful/

[@falconiqx]

h is the distance between the two points you're using to find the slope. If you are trying to find the slope of a straight line then h can be as big as you like, but if you're trying to find the value of the slope on a curve at X, then you want the h to be as small as possible. It could be 10, or 1, or 0.1 or 0.001 etc... etc... and as it gets smaller you'll get closer and closer to the exact answer.

[@bsivoljr]

Lol you def need your book for practice to say the least. Khan Academy has been the single most effective study supplement I have ever encountered. So many mind booms

[@magnuschanduru6173]

I am wait for such kind of teacher like u. U r superb.

[@gocanadayayyy]

THIS IS SO INCREDIBLY HELPFUL. I took the IB program and the way our school runs it we finish math a year early. I haven't taken calc in a year and I'm starting university and taking calc next year... eek. Unfortunately my calc notes are just a bunch of examples explained in class (explained very well, I might add) that make no sense now. Thank goodness for these videos or I'd be so lost next year! It's all coming back to me now.

[@davisjohn-d6h]

I'm currently a software designer and egineer. I haven't reviewed Calculus in a couple months, than you Sal for reviewing this, your great at lectures.

[@antoniro13]

I always asked myself what kind of software you use for writing...

[@eurekanunez2376]

THERE ARE SEVERAL WAYS .... YOU CAN GET A TOUCH SCREEN PC SUCH AS MICROSOFT SURFACE PRO AND USE A SOFTWARE THAT HELP YOU TO RECORD THE SCREEN OF YOUR SOFTWARE, CAMPTASIA STUDIO IS A GOOD CHOICE......

[@geethakochukunju3757]

Paint

[@orion_222]

@@eurekanunez2376 can u stop shouting im trying to listen

[@ranjitn159]

@@orion_222 some people don't know that BLOCK letters mean shouting!

[@r4fa3l59]

It's Paint...

[@busenurylmaz9706]

Thankful for the subtitles, eng is not my native language but your explanation is really clear.

[@larryhernandez5062]

Very good definition . I do like how He explains the definition using visualization by definition . . . .

[@hedonism13]

I swear to God, 13:15, it just suddenly clicked. Like in the old movies where the lightbulb goes on over your head. Thank you, thank you, THANK YOU, I FINALLY get Calculus. You are awesome, my only regret is I have only one thumbs up to give.

[@johnsono7651]

wow! beautiful explanation. Got me clapping in my school library

[@shreerangvaidya9264]

The way you explain it makes me feel like this could be taught to kids easily.

[@tony0964]

Great. it's better than the standard-def version. Just a tip, turn off the noise suppression and/or cancellation on your audio software (your voice will be better quality)

[@Ulquiorra191]

I was absent in class this day and the book's explanation makes no sense.... thank you so much.

[@DaveKings]

Well Donald, I have taken it upon myself to congratulate you on this comment. Knowing that just changes every aspect of reality as I have grasped it since the day I popped out.

[@TheEastflowers]

I'm from Sweden and I don't even fully understand english. Still, this video helped me a lot, 5000 times better than my teacher. Got an A on the test, thx so much!!!

[@bonsh928]

Im 12 and this is the first time I have understood any concepts in Calculus, Newtons Principia all the way

[@MrPraise88]

thnks for this explanantion!!!..I thinks this is the best explanation about how the how the first principle of derivatives was exist!!...my lecturer is suck!!...she dose'nt explain how the first principle of derivatives come out....mostly teacher just directly jump to the example of Question that applied this very concept....A FULL CREDIT for U utubers!!!! thnks....

[@goodacademics]

Suggestion: your may want to use other alphabet instead of "b" for the second x-value because it may create confusion with the "b" in the f(x) = mx + b, where that "b" is the y-intercept. Good work!

[@HadiExtreme]

Thanks again. You helped me understand physics and now you're helping me again. You can explain way better than my math teacher.

[@diceman31]

why is it that every youtube instructer explains it 10 times better than any professor I ever had?

[@PJDguitar]

A line parallel to Y is one going straight up, and therefore has an undefined slope. For every value of Y there is only a single value of x.

[@TheRygatto]

OMG this is much more understandable than my teacher! Thx Mr. Khan for your fantastic vids!

[@Austin_Schulz]

Shot game: Every time Sal says "Let me try a different color." take a shot. Every time said color is magenta, take TWO shots.

[@pauljs75]

For a real challenge watch "Elephant's Dream", take a shot anytime the name Emo is mentioned.

[@JP-fp3hm]

+Papa Schulz Already doin' it!

[@Hwyadylaw]

+Papa Schulz Every time he says something twice

[@SoberBro]

Hey! No drinking and deriving! Edit: I now realize that "derive" is not the act of taking a derivative.

[@Telamon8]

;-; but I like my liver

[@VFB1210]

Great video! Altough when you started calling x0 "X naught" you confused me for a second by making me think you meant "X not"! I spent about three minutes trying to figure out where we started using Boolean Algebra!

[@BZakaTheCoolGuy]

Knowledge is a power which breaks the shackles of ignorance.

[@Sputnik966]

I highly recomend Khan academy to anyone who wants to teach them self a new subject. But yea, it would be good to get used text books. Text books are geat.

[@nriab23]

You have the ability to explain more in 10 words than what some people can't explain in 1000

[@Altare1994]

The limit of the function as it approaches 0 from both or one side, because at f(0) the function is undefined, Does Not Exist. Therefore you find x coordinates and their y counterparts as the function gets closer and closer to 0, eventually determining the LIMIT

[@ianmotley1992]

This is brilliant. This is why I love youtube!

[@SarinaSaman]

This is so good explained, i knew it before but I understood it from here. Thanks a lot.

[@DeepeeMe]

HD is awesome on your videos ;D Now the lines aren't scrathy and 'pixelled' now they're smooth and is blured - really good ;D

[@gohoggyourself]

This video has been the keystone in my scattered knowledge of derivatives

[@johnkirkhoughton1]

I wish I had you as a teacher the first time around.

[@paoloparker8991]

perfect video, you can't make a clearer explanation than this one

[@andyh8700]

Awesome now I have a better understanding of Derivatives!

[@steveocken]

1. The tangent line to a curve at point P is described as a line that just touches the curve at that point. That is both vague and incorrect. 2. In the last frame, f'(x) should be f' (x_0)

[@sophc193]

the h = delta x thing was veeeeeery helpful.

[@vovven88]

Sal, I spend more time with you then my friends! You are my dearest friend ;)

[@Geek4Lif1]

Thank god for Khanacademy. My teacher was terrible at explaining derivatives today. Everyone looked like Homer Simpson after she got done teaching us.

[@satisfiction]

6:45 The most colorful graph of x² I have ever seen.

[@KechupyDeath]

hold shift to draw straight lines (vertical and horizontal) hold space so you can grab the page and move it about (i'm assuming that's PS)

[@1996sagark]

I have my holidays going on But watching your vids is much more fun than just time passing or playing psp ahah And most importantly I gain knowledge haha (Y)

[@pieyouel]

before watching his vids. I feel like the most sucking student in math in our class. After watching his vids, i feel like i'm the most intelligent. ^^ Man, you are soo00oo AMAZING!

[@007MrYang]

I would love it if your webpage had practice exercises for chemistry and physics.

[@donaldlofton5041]

Greetings everybody. I just turned 11 and I know how to do this stuff. I love to do math on my free time and go to the library daily and look at all the advanced mathematics book.

[@deugle]

I really enjoy your videos but would appreciate if you wrote a bit larger when using this new HD format.

[@2048scotty]

wow, this makes insanely good sense! Where were you when I was barely passing Algebra in HS?

[@abezerianos1]

The limit of f(Xo+h)-f(Xo) over h is not equal to f'(x) but the equal to f'(Xo).

[@parnikag99]

I'm in Grade 7 and I understand this! Good job!!

[@osama_alsafi]

God bless you man. Hope it will stand up for you on that DAY

[@sezanjay]

If the slope was on the negative side of the chart, would you then minus the power or still +1?

[@0109220h]

It makes sense!! Thank you!

[@jacque4572]

You are an angel! Thank you so much for all your wonderful videos, you make education and learning so accessible and so much easier. I can't say how grateful I am to finally understand the meaning behind the equation of a derivative!

[@BZakaTheCoolGuy]

That is a great age to start, but don't forget that if you get focused on too much calculus and stuff above your level, you would forget about your other subjects, I would just get up to grade 10, and then start practicing calculus :) Good luck bro!

[@Ruwenzori100]

This video helped me to understand derivatives. Thanks for breaking it down and making it so simple.

[@SharxKL]

Thank You!!!! Helped a lot!

[@vtron9832]

In a curve, exactly what points do you use to find the slope and how far apart do they have to be?

[@deependraverma4382]

just take two points on the curve and join them to get a secant line and then find the slope using rise/run, However, if you want to find the slope at an exact point then you should take the derivative of the equation of graph and put the point on the x-axis on which you need to find the slope in the derivative. eg. graph is y=x^2 then the derivative is 2x. Suppose you need to find the slope at x=1 then put the value 2(1)=2 that's your slope.

[@pageerror404]

Me: Excuse me, I'm having trouble understanding exactly what a derivative is. Math Teacher: It's f(x+h) - f(x) / h Me: *sigh* Seriously I spent a while semester pretending to know what a derivative meant and now I learned it in 15 minutes lol.

[@SwellBread]

your lessons exude intuition!

[@PJDguitar]

y is equal to f(x) any time an equation says something like f(x)=x+1 its the same as saying y=x+1 since f(x) is = y then we can say if our x value is 3 its f(3). Since we are evaluating the equation at that point. So if our x value is a our why value if f(a) y is the dependent variable and it's position depends on what we are evaluating x as.

[@nicoelyorugua]

Best viedo ever

[@GustavoRivasMendez]

You make math look beautiful :D

[@dillonh2118]

Once again Khan saves the day

[@AMrTheAn]

If you'd like to understand calculus, learn these subjects in order: 1. Basic math/Pre-Algebra 2. Algebra 1 3. Algebra 2 4. Geometry 5. Trigonometry 6. Pre-Calculus 7. Calculus You're 11, which means you have a better start than I did at becoming a mathematician or scientist. After 2 weeks of watching Khan Academy videos, I have managed to learn Calculus, and I am 14.

[@bobby_mathews]

wow thanks man that's such a superb explanation of derivatives

[@1073601]

this sure is a lot easier than the previous lesson

[@Loriixoxo]

the HD videos are much better and easier to follow than some of the old videos, because the lines used to write are crisper, rather than all sketchy. I'm so glad you're taking the time to re-do some of the videos in HD quality. Did you just get a new program to make your videos with? Before, your pointer looked like a regular arrow mouse icon, and now its a crosshair... also, I think you were using a mouse before to do your videos, and now it looks like you're using a tablet. Just curious.

[@BearsFan054]

wow HD is awesome!!!!! Thanks Sal!

[@randomguy_ts10]

Absolute brilliant...

[@Sputnik966]

Thats a good age to start, thats when i got into calc.

[@sanskritisarraf]

Understood thankyou

[@connorhogan9469]

Khan Academy - As always, studdin' on the daily.

[@antcolony23]

incredibly clear, thank you!

[@mrupdater009]

Sir, Please upload full series of video lecture of this subject. Please sir upload Basic to Advance label with some good exerciser. I hope your uploading video tutorials will be help me and other to solve some complicated exercise spontaneously.

[@allenllewellynkra]

Very good explaination Mr. Khan

[@ajeanville]

Great video, I finally understand this 😊

[@kjezier]

if you are really from 1996 it is so cool you pracice yours math skill in that age

[@sean20412041]

Grace - you aren't finding the limit of 0, you are finding the limit as the distance between the points approaches 0

[@NTMihaila]

I think it's a bit odd that I found this video to be truly enjoyable. Fun stuff, really.

[@AtikaTahsinSaba]

The slope of tangent line is consistent the whole way through the function.

[@artashes999]

Khan Academy AND Math tutor DVD are fucking amazing, i think everyone should try both of them out.