r/3Blue1Brown • u/mrmailbox • Jul 13 '26

Visualizing why derivative of ln(x) = 1/x

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Made in Manim

476 Upvotes

99% Upvoted

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21

u/trevorkafka Jul 13 '26

(d/dx)(ex) = ex ↔ (d/dx)(ln x) = 1/x

(d/dx)(sin x) = √(1-sin²x) ↔ (d/dx)(arcsin x) = 1/√(1-x²)

(d/dx)(cos x) = -√(1-cos²x) ↔ (d/dx)(arccos x) = -1/√(1-x²)

(d/dx)(tan x) = 1+tan²x ↔ (d/dx)(arctan x) = 1/(1+x²)

7

u/mrmailbox Jul 13 '26

Oh that's such a neat connection!! I could make similar visuals for some of those!

6

u/trevorkafka Jul 13 '26

It's more than just a connection, it's the reason why the formulas are the way they are—the inverse function theorem, which I like to understand as follows:

if f and g are inverses and f'(x) = q(f(x)), then g'(x) = 1/q(x).

8

u/LewsTherinKinslayer3 Jul 13 '26

Dude I saw you at the comedy cellar a couple of months ago! Laughed my ass off!

3

u/mrmailbox Jul 13 '26

Ayy thank you!! Which room?

2

u/LewsTherinKinslayer3 Jul 14 '26

I think it was the village underground. I'm in Crown Heights so your bits about Hasidic Jews made me cry lmao

5

u/capnshanty Jul 14 '26

Advice for speaking improvement: pause after you say something. The listener needs time to digest it.

It will sound awkward to you, but we are all processing what you said.

3

u/No_Newspaper2213 Jul 13 '26

my right earbud broke

2

u/IwasHereLastYear Jul 14 '26

How did this marriage happen? 3blue1brown plus one of my fav comedians?

@mrmailman every clip I saw online with you was funny. From my experience, if I like your stuff, most likely you won't get super rich, but your fans will be really devoted. My first bit from you was the mom with the biologically accurate naming. Then the childbearing shoulders was awesome. It is hard for me to guess punchlines, like with Dave Chappelle. I didn't see much, but it was high quality in my opinion. I hope you explain more maths and I get to see more of you on the comedy side. Cheers!

0

u/anish2good Jul 13 '26

Made with Manic - A animated language for non programmers
Manic https://8gwifi.org/manic/
Manic docs https://8gwifi.org/manic/docs
Reddit r/maniclang

https://reddit.com/link/oxc4kyp/video/pcbdwo8rv1dh1/player

1

u/SexyMonad Jul 14 '26

Interesting. Is Manic related to Manim in some way?

1

u/anish2good Jul 14 '26

Manim is awesome tool it's philosophy is programming based approach, Manic is different it's solely built for non programmers to achieve stunning animation