The paradox of the derivative | Chapter 2, Essence of calculus

What is an "instantaneous rate of change" when change happens across time?
An equally valuable form of support is to simply share some of the videos.

Note, to illustrate my point for the target audience of a new calculus student, I discussed a hypothetical speedometer that makes distance measurements over a very small time. Interestingly, most actual speedometers in modern cars work by analyzing the induced current of a spinning magnet, which is in some sense the universe implementing the derivative.

Thanks to these viewers for their contributions to translations
Dutch: @LFWarsen
Hebrew: Omer Tuchfeld
Italian: mulstato
Vietnamese: @ngvutuan2811

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Various social media stuffs:

[devinneal]

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This is not just math. This is art.

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[ozkaa]

watching this series has made me fundamentally question the quality of the education I received at school growing up. It's exposed how badly we were explained these concepts in class. I did so much calculus at school without ever being given a real understanding of what i was doing. And then I wonder if the same maybe applies to all my subjects at school. maybe my whole education was actually entirely sub par and I've fallen far short of my potential as a result lol.

[ramitello]

"I would use the letter "d" for distance, but that guy has another full time job in Calculus" Lmao

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[razvanefros]

0: Oh? You're approaching me?
dt: I can't beat the shit out of you without getting closer

[firen]

I'm not sure which one I find more amazing: the math itself, how clearly you explain it, or work you put into the animation.

[tannerkent]

Those aha!" *click* moments that were so rare in my University calculus classes are so frequent in these videos.

[dripcat]

everyone: "no one can calculate instantaneous change. it's totally nonsensical"
fathers of calculus: "so I'm gonna do what's called a Pro Gamer Move-"

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Keep up the good work!

[paulmatsumoto]

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[Carsonlego]

It literally took me months to understand this video but I’m super glad I do now. Thank you so much 3blue1brown

[lokmost]

Nice video.
My University's teacher used this to intoduce us to derivatives

[BGbaas]

Wow I've almost obtained my bachelors degree in Aerospace Engineering and I finally get to see why the derivative of a polynomial is the way it is, thanks for your great videos and insights!!

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[arnouth]

I know it’s a bit late, but may I just say that this is an absolutely phenomenal series. It really helped me understand calculus in a way that just didn’t happen at school.