The other way to visualize derivatives | Chapter 12, Essence of calculus

A visual for derivatives that generalizes more nicely to topics beyond calculus.
An equally valuable form of support is to share the videos.

Essence of calculus series:

Really nice applet made based on this video by Reddit user Larconneur:

Music by Vincent Rubinetti:

Timestamps:
0:00 - The transformational view of derivatives
5:38 - An infinite fraction puzzle
8:50 - Cobweb diagrams
10:21 - Stability of fixed points
13:38 - Why learn this?

Thanks to these viewers for their contributions to translations
Hebrew: Omer Tuchfeld
Vietnamese: ngvutuan2811

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3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted on new videos, subscribe, and click the bell to receive notifications (if you're into that).

Various social media stuffs:

[fluiypj]

Now I just need a video entitled “what they teach you in calculus” and I’ll have the sum of human knowledge

[scbl]

Him: “Picture yourself as an early calculus student, about to begin your first course.”

Me, an early calculus student about to begin my first course: ...

[UPDATE]: 2 years later looking back at this video and the responses to my comment, my passion for math and physics has taken a bit of a dive but still there! To all the people who said such nice and encouraging things, thank you! People like you are what keep me going in today’s world. I passed Calc 3 with a 101% and Differential Equations with a 94%, onto PDE’s now and it’s going great so far!

[pipdang]

To be honest, this feels like a video about calculus for people who are way past calculus.

[bluebrown]

The brits among you yell at me,
for how I say the letter "phi".
But ask a Greek, they won't deny,
there's something odd in saying "phi".

[alexdowad]

...Just realized that 3Blue1Brown is the same guy who did the multi-variable calculus course for Khan Academy. That is probably the best math course on KA!

[NightmareCourtPictures]

This will help me make my redstone trapdoor.

[MarkChimes]

Man... I have a masters in maths and your videos still manage to blow my mind.

What a beautiful way of looking at derivarives, and what an elegant application to that fractions problem!

[AndrewGazz]

"Clearly you watch math videos online"

Finally! Validation!

[santiagoerroalvarez]

That "next video" tease at the end broke my heart. I was so excited by the idea of a 3B1B video on holomorphic functions and the jacobian determinant, only to discover that, a year and a half later, it still doesn't exist.


It's sad that my first comment on one of your videos is just a lame upload request, so here you go: You have made me truly fall in love with math. Don't get me wrong, I've always liked the subject, this isn't one of those math redemption stories. But I used to like it in a much more different way, only appreciating the challenge that trying to arrive at a result poses. Your videos have totally changed my view of math, from symbols that obey certain rules and prove to be a useful toolkit, to something valuable in its own right. Something dynamic, endlessly explorable and, ultimately, alive. With your marvelous way of communicating, you have sparkled my curiosity and made me eager to learn, every day, a tiny bit more about math. And, for showing me the immense beauty this subject has to offer, I cannot thank you enough.
Thank you for every moment of your time you have invested in this channel. You have changed my life.

[a-aronpre-sent]

People who create quality content like this for the world to feel in awe about are people who make the world a better place. It opened me to appreciate and see beauty where others see despair and agony—in maths.

[Astronomy]

calculus teachers hate him!!
learn how he graphed equations with this ONE SIMPLE TRICK

[harryb]

Now that I have done calculus and watched this video, I now know everything there is to know in the universe

[BenRowleythetheoryofeverything]

Every time i get a notification for 3blue1brown i know my love for maths is about to be reignited

[kjekelle]

0:00 intro
1:35 the standard visual
2:22 the transformational view
5:38 application
9:45 graph vs transformation
13:32 the point
14:41 outro and sponsor

[jaday]

Currently watching this video about calculus instead of actually studying for my calculus exam tomorrow

[superjez]

You should do an Essence of Complex Analysis series.

[AJ-ermy]

'Picture yourself as an early calculus student, about to begin your first course.' Haha, that's me this upcoming school year. Watched through these videos on a whim and have really appreciated them. It's made calculus seem intuitive in a way that my friends who took it through the traditional school route haven't been able to garner. I really appreciate this and can't wait to start applying the concepts I learnt through this series!

[shubhamvishwakarma]

You made me understood in 15 minutes, what my teachers failed to explain me over an year.I wish if I had teachers like you.

[MathManMcGreal]

Love your insight on "conceptually lighter" topics like this coupled with your calm voice and chill music. It's like a soothing math meditation...

[conoroneill]

I find it really interesting how two at first seemingly different questions can end up having a strong link - just the other day I was looking at the logistic map and its attractors, and was trying to find solutions at various inputs, and figure out which of those inputs were stable and which were unstable. I wish I'd seen this video before then - I was hopping between using calculus and using the graphical intuition, without a whole lot of connection between them, which was kind of frustrating. (I wish I had enough programming knowledge to try and map the logistic map in the way you did for the 1+1/x function here, so I could see it visually.)

Actually, I'd really like to see some 3b1b videos on Chaos Theory, because its the kind of combination of visually accessible images and deep math that would work well in a 3b1b video.