The change of position over time is velocity. The change of velocity over time is acceleration. The change of acceleration over time is a jerk. The change of a jerk over time is an election.

My calculus professor is sending us links to these vids instead of having a zoom lecture. So congrats on teaching MATH155 at Colorado State University.

The 4th, 5th, and 6th derivatives are Snap, Crackle, and Pop, respectively.

4:48 : I have to correct this, because it confuses my students too. You said ‘A negative second derivative [of displacement] indicates slowing down’, but that's only correct _if_ the velocity is positive. As you noted in the video on derivatives, a negative velocity means that you are headed in the negative direction. And in that case, a negative acceleration means that you are _speeding up,_ with the velocity becoming even more negative, while a _positive_ acceleration means that you are slowing down. If you want a quantity that's positive when you're speeding up and negative when you're slowing down, then you need to take the derivative of the _speed,_ that is of the absolute value of the velocity, so the second derivative of the total distance travelled, but _not_ the second derivative of the displacement. (Arguably, this fits more with the way we use the word ‘acceleration’ in ordinary language, but the technical meaning is the second derivative of displacement.) As an aside, this disparity becomes even more extreme if you're moving in multiple dimensions of space. In that case, the displacement, velocity, and acceleration are all vectors, and it doesn't make sense to say that they are positive or negative as such. Then the speed is the magnitude of the velocity vector, and the derivative of the speed is again positive if you're speeding up and negative if you're slowing down. But now it's also possible for the derivative of the speed to be zero, even if the acceleration is nonzero! In that case, the speed is constant but the velocity is not, because you're changing direction.

I think Korean is funnier here. After "velocity", you just add "가". Displacement = 변위 Velocity = 속도 Acceleration = 가속도 Jerk = 가가속도 4th derivative = 가가가속도 5th derivative = 가가가가속도 6th derivative = 가가가가가속도 ... nth derivative = (가)^(n-1)속도

Who dislikes this video is a 3rd derivative

Position Velocity Acceleration Jerk snap Crackle Pop

Beautiful explanation, visualisation, and most importantly, the simplicity you always use to explain complex terms. Love it

Nowadays everyone is releasing non-episodes in the same universe. First there was _Rogue One: a Star Wars Story,_ and now we've got _Higher Order Derivatives: a Calculus Story._

3:47 "Interestingly, there is a notion in math called the 'exterior derivative' which treats this 'd' as having a more independent meaning, though it's less relatable to the intuitions I've introduced in this series"

This channel deserve more subscribers

-5 >> Absounce -4 >> Abserk -3 >> Abseleration -2 >>Absity -1 >>Absement 0 >> Displacement 1 >> Velocity 2 >> Acceleration 3 >> Jerk 4 >> Jounce I really had a hard time understanding Less than 0 and more than 2... Can anyone make a video to explain it all??

Hello Grant, I really admire your videos as you can see I am watching these again even after two years. Please do a series of animations on Complex Analysis and Transforms (laplace, Fourier and Z).

Ces vidéos sont supers..je conseil ; grand merci 3bleus 1marron..

You should definitely do a video on the gamma function and fractional derivatives.

Thank you very much for this video! It was quite informative seeing how the 2nd derivative can be a comparison between two sets of 1st derivative value multiplied by some dx

thank you very much, I have been using your series on calculus to help me study for my final. you have helped me better understand some things I didn't understand in class, such as how limits and implicit differentiation

I just want to say:thank you! I learned a lot

I took Calculus (1 2 and 3) back in high school. I am watching this series for probably the third time because these were all the same intuitions I had that helped me understand the subject the first time around. Keep up the great work with all your videos!

0:00 intro 0:39 derivative of the derivative 1:53 notation 3:58 intuition 5:05 outro

Very smooth and concise explanation!

It looks like this series is going to end the day of my AP Calculus exam. Thanks for helping me study +3Bue1Brown

Excited for the main event! Thanks for explaining this

incredibly amazing as usual.

can u do an essence of differential equations? ubhave no idea how much i love these

Awesome explanation of order of derivatives. Intuitively explaining rate of change of slope as second derivative.

the double upload made my day, thanks

3:31 much clear now: the second derivative is treated as the difference of two first derivative: if its positive, it increases

Brilliant video ✨ Thank you so much for it

Your videos are so cool. Love them 👌🏻

tenho vontade de chora de tanto q amo esse canal it means i love this videos so much that i wanna cry

I love this channel so much Thank you so much

really loved it especially the jerk part, we're really taught this stuff in school

Amazing explanation !!!

Thanks man this is so helpful

you must be some kind of god...thanks for these awesomely illustrated and explained videos Sir!

Awesome work...!!!

thank you for this great video

Oh my gosh, thank you. I finally understand now. I was having a hard time figuring out the relationship between f(x), f'(x), and f''(x) but the displacement, velocity, and acceleration explanation made so much sense.

Another excellent video.

Can't wait for the next chapter

The "change of how the function changes" really made it click there. Thank you.

i love the small pi. Thx bro

So intuitive !

3:17 Why is d(df) proportional to (dx)^2?

3b why no quote at the beginning of this video? I love all those quotes you had in other videos

An extra video... nice

Great video👍. Can you make videos on optimization with linear programming?

good man 3blue1brown

I will translate the caption of this video into Portuguese. The video lessons from this channel are very good!!!

Thanks

So i was studying the potential energy vs position graphy and there i encountered that second derivative of potential energy will give you the points of stable,unstable and neutral equilibrium. but now one told me how? So i searched the internet and youtube and here the search is end with this video.now i know why.so a heartfull thanks to creator of this video.your helping hand is changing the world in positive way.keep spreading love and knowledge.😊

Will you be doing any videos on non-integer-th derivatives? Or is that too far removed from fundamental calculus..?

two videos in one day?! is it christmas already?!

Could you make a video on THE ARC LENGTH OF A CURVE?

Thankyou very much sir

Thank you😊

this notation was really strange for me, so thanks for clearing that! :)

All hail our great leader 3b1b.

Everytime I see your videos I get a lightbulb moment. Suffice to say soon I wil run out of light bulbs to imagine lol. Thanks for the amazing videos.

I've first learned derivatives years ago, but I've only just figured out how the (df/dx notation works). For some reason, I've always thought that d^2 f / dx^2 was d^2 f / d (x^2) and that just made no sense to me

Great for students animations rocks !!!

If the 2nd order derivative is positive, the function's graph "holds watter". If it's negative, it doesn't!

Please upload a video on differential equations and singularities.

Rip me I watched the footnote after chapter 10 lol

this is so well explained and intuitive. why can't all teachers teach it this way instead of boring formulas and telling you to stfu when you ask why this is so, which is what my teacher did all the time? Did he have to be such a d^3s/dx^3 ?

Would anyone plz tell what derivatives greater than degree 2 mean mathematically like 2nd derivatives tells rate of change of slope then what does 3rd or 4th or nth derivative mean.

3:54 does anyone know why (dx)² becomes dx², not d²x²? I know everyone writes second derivative like that, but I'm just curious. Is that simply because dx² is almost same as d²x²

to push it a little farther 4th derivative of position vs. time is jounce

We worked with second derivatives all semester but I saw this notation on my calculus final and had no idea what it was.

Merci!

thank you

For best understanding why the derivative of accleration is called jerk imagine a computer driven lathe. To move the tool to position you want smooth movement so that the tool does not break. If your movements jerk is too much then the movement is not smooth but it's jerky. Another example of jerk is in an amusement park. If you ride the coffe cups the movement of those cups have sudden jerks in them and if you graph the movement function and calculate jerk you find out that jerk is high on those parts of the movement. So the name jerk is a very good description what changing acceleration means. Btw. Human's sensory system work well in acceleration and so smooth acceleration does not cause any feelings in itself. For example your inner ear does not react to gravity. A non changing acceleration field does not register. But increase jerk and you inner ear starts to function. That's why amussement park rides use high jerk to cause effect in humans.

Beautiful

For the weird people who want to know the ones after its in this order 1)Position 2)Displacement 3)Velocity 4)Acceleration 5)Jerk 6)Snap 7)Crackle 8)Pop

After watching your videos I felt if your channel were exist back in 2004 when I was a college students.

Integration by substitution Non added but it is chain rule integrated

Why does no one talk about jerk with cars. Surely that is the effect of having higher torque? You can jerk the acceleration more quickly

Where did you get the function of the distance of the car in terms of time?

Hey, Professor Bertrand! So in general, for any Taylor polynomial, the coefficient c_n (the coefficient of x^n) controls the nth derivative of that polynomial evaluated at 0.

Incredible

the best!!

Please clear between derivative at a point and derivative curve

hollyshit TAYLOR SERIES!!!

Love you

❤Helps a lot,love from China🎉

original: position velocity (1st) acceleration (2nd) jerk (3rd) snap / jounce (4th) crackle (5th) pop (6th) Lock (7th) Drop (8th) Shot (9th) Put (10th)

What does fractional derivatives mean visually??

What software did you use for animations?

Somebody explain me here please. Why is d(df)= (Some constant)(dx)^2 ? I mean the change in slopes is df2-df1 right? I don't understand how it is some constant - DX^2.

Can I find the music anywhere?

snap, crackle, pop

_If Displacement-Time graph of a ball moving, follows the function e^x exactly_ _Then, that is the most interesting type of motion in this Universe_

*JERK* as in "a quick, sharp, sudden movement", not "a contemptibly obnoxious person."

ah if only you had posted this video when i was taking calculus class in my freshman year

Wat software is used to create this video ?

I found out about Jerk when i thought about how acceleration on earth is proportional to 1 over distance squared. So there is a rate of change of acceleration as you fall..not sure if its jerk or even a higher order.

Why we equate zero of minimum degree term in given equation to get tangent at vertex and why equate zero the coefficient of higer degree of x to find asymptote parallel to x axis Sorry sir these questions are out of this vedio bt if may possible so please solve my query.

I just realized this is directly related to Fourier series!

How do you animate these?