Differentiability and continuity | Derivatives introduction | AP Calculus AB | Khan Academy

[@tanishql1441]

This is just so amazing. This intuitive approach is not taught in high schools.They just give the formula, but never tell us why it's true which makes students slower hate calculus. You are amazing. This vedio should be shown in all schools and teachers should learn how to teach from this.Hats off to you. 👍👍

[@ian.ambrose]

True. I love it so much.

[@sunandak71]

You are amazing in teaching the depths of concepts. Thankyou for this video :)

[@lingeshwaranramamoorthy626]

just elegant and smooth

[@mulisanemadzivhanani3793]

khan academy , you are a star

[@kamleshmehta7165]

One of the best educational channel

[@jack-bn3zh]

nice crosshair pointer. great lecture. thanks

[@ashishprajapati7734]

after seeing this video , i am your​ fan

[@Emc4421]

AWESOME VIDEO. HELPED ME SO MUCH THANK YOU

[@thomasc7526]

Crosshair looks like I'm playing csgo

[@qasimwaraich388]

Could u show if it IS diferentiable???

[@prernasalunke4126]

Thank u Great video

[@ChadfusiousSays]

Sal how are you making the straight line at 8:50 ??? It has been bugging me so bad to write a straight line on smoothdraw3. I know you can hold shift to make a straight line but placement becomes and issue. How are you placing a traceable line like that???

[@louisfoley6955]

The point made for the absolute value graph, that there are many tangent lines that can pass through x = c, can be applied to any point on a curved graph as well. So I don't think it's valid reason to justify the vertex of an absolute value function not being differential in that aspect. I was a little confused when he said that.

[@zanyarraouf5770]

no it cannot, it only applies to sharp edges (cusps)

[@rejathsimon9001]

Thanks for the video😄😄😄

[@themasculinetransformation]

Hard to understand language barrier but still I learned some thinks at least

[@GlitterB8]

Very helpful 😀😀

[@openroomxyz]

Can a function be smooth , not a broken line f(x) = abs(x), and non differential, what would be some more non obvious case?

[@mxlexrd]

If you mean smooth in a technical sense, that's not possible because the definition of smooth requires the function to be differentiable. If you mean smooth in an intuitive sense, try f(x)=cuberoot(x). This function is "smooth" but not differentiable at x=0.

[@19-gouthamkumarreddy58]

A teacher have to be like you,and you made all to believe all that math is not to find - "x" ,but math is to ask "wh-'y'" ?

[@5dots297]

Pointer is way too big

[@goldenboy7697]

Could we just use the power rule on both sides and see if the derivative is the same? to see if it is differentiable at that point?

[@vinaykumarhs5509]

I Have a Question (more like confirming),.......so, is there are situation where c can be continuous but not differentiate, Then the only Situation I can Guess for that to be true is ALWAYS a straight line(a Linear Function)

[@naseemmalik7301]

plz sir upload a theorem if f is continuous then inverse of f is also continuous

[@konvictz0007]

hi I agree the pointer is too big and distracting, it would be better if it was like how it was before.

[@sarakavi84]

Can u draw the derivative curve of first two graph sir .. was a great explanation sir..

[@mynameisZhenyaArt_]

mouse pointer (cross) is too large

[@zahraadyab3059]

Thank you

[@anime_dattebayo1906]

NICE

[@sansamman4619]

thanks for the amazing videos but just stop!!! I feel weird because I'm getting entertained by something that should be educational and boring...

[@YouTube.KtBlush]

3:24 😭

[@SoumilSahu]

PLEASE reduce the size of that pointer. The explanation is amazing, but the huge X is VERY weird to look at!!

[@99hockey54]

How about you just appreciate his lessons -free of charge-, and quit whining like a little bitch?

[@romeorohng6163]

I thought you can only find tangent line of curves and not straight lines, so if the function is continuous but you cant draw a tangent line then there is no derivative, so is not differentiable?

[@AkhilKumar-ci6pb]

its not finding tangent but finding the slope of tangent at a point on cure, for a st line slope is constant even if you differentiate you get the same value anywhere

[@biz2911]

hi!

[@lazybacon5282]

Hi

[@jaydenlewis1134]

first again

[@jaydenlewis1134]

hey Khan if ur online pls reply...

[@tyjejones4903]

You can 1:®®®π^`£ I AA AA Wg ##### VvVScGz $ your. z G#z

[@mahaimtiaz5578]

125th view!!!

[@Dr_Techo]

Your definition of the derivative of f(x) is totally wrong!

[@HilbertXVI]

TECHO VINCENT POWOH Nah you're just stupid

[@AkhilKumar-ci6pb]

we use h as difference bw x and c so notation is different not wrong think before u act

[@fahimkhan-tj1cu]

How is it wrong?at least i didnt find it wrong.

[@goldenboy7697]

it is definitely right, there are two limit definitions of the derivative.

[@ankitaaarya]

Thank you