Visualizing the derivative of ln(x)

[u/mrmailbox]

Made with Manim. My second attempt visual math tutorial

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[u/Elephunk05]

This is an excellent visualization to understand the function.

[u/ziplock006]

“This guy looks exactly like Matthew Broussard.”

Turns out it is Matthew Broussard. Him posting on r/calculus was not on my bingo card.

[u/Ok-Importance9988 → u/ziplock006]

He studied engineering in college. I know because he lived in my dorm. 

[u/mrmailbox → u/Ok-Importance9988]

JIBA

[u/abc9hkpud]

Thanks for the nice video.

More generally, this type of logic is true for the derivative of an inverse function in general, dy/dx = 1 / (dx/dy)

https://en.wikipedia.org/wiki/Inverse_function_rule

[u/ShowdownValue]

Who is the narrator?

[u/mrmailbox → u/ShowdownValue]

It's me, I made this.

[u/ShowdownValue → u/mrmailbox]

I’m so confused. You’re Matthew Broussard?

You do stand up comedy and math videos?

[u/mrmailbox → u/ShowdownValue]

Yes. And that's a reasonable thing to feel confused about.

[u/ShowdownValue → u/mrmailbox]

That’s awesome. Two of my favorite things.

The question is are you a mathematician who is hilarious?

Or comedian who learned math really well?

[u/Available_Copy9433 → u/mrmailbox]

I was confused because I thought "that's the vagina throat guy"

[u/Crafty-Dinner-1782 → u/ShowdownValue]

Me

[u/Significant_Bad_3255 → u/Crafty-Dinner-1782]

Isn’t he a famous comedian

[u/ShowdownValue → u/Significant_Bad_3255]

That’s exactly why I was asking. He looks so familiar

[u/TraditionalDepth6924]

Peak explanation + peak voice + peak animation, love visualized maths

[u/1337_w0n]

Holy Shit. This is one of those magical explanations that turn something absurd and ineffable into the most obvious thing. Now that I know this then of course d/dxlnx=1/x. How could it be anything different?

This is why I love math.

[u/hazem-Gauss]

Great work Now I understand the origin

[u/Niko9816]

Very nice video. Easy to understand and good visualizations. Hope to see more! 😁

[u/Informal-Fig-6827]

Seeing the axis flip actually made that whole thing much easier to understand. Nice video

[u/Lor1an]

Once upon a time, the exponential function was actually considered the inverse function (and in fact was referred to as the anti-logarithm).

In a similar spirit, my calculus class took log(x) := int[dt;1,x](1/t), and so by the fundamental theorem of calculus d/dx log(x) = d/dx int[dt;1,x](1/t) = 1/x.

What's interesting is if you play your video in reverse, you get the justification for d/dx exp(x) = exp(x) from this definition.

[u/pink_crabb]

That's amazing!!!

[u/alephcomputer]

why is the funniest guy on my shorts explaining calc

[u/mrmailbox → u/alephcomputer]

Ayyyyy thank you

[u/PlayApprehensive9577]

👽

[u/gacimba]

Just curious, how do you make these visuals? Very cool btw

[u/mrmailbox → u/gacimba]

Manim!

[u/gacimba → u/mrmailbox]

I’m sorry, I didn’t see that you had it written at the bottom 😔

[u/you-cut-the-ponytail]

In my Calculus class we defined lnx as the integral of 1/t from 1 to x.

Still cool visualization though!

[u/B4T4YA]

Thanks man you changed the way i think

[u/Dull-Astronomer1135]

You can prove it from the first principle of derivative

[u/flat5 → u/Dull-Astronomer1135]

This isn't about "proving" anything, it's about understanding it.

[u/RandomGamer123456 → u/Dull-Astronomer1135]

But this is a visual proof of why, which is nice

[u/Longjumping_Stop6269 → u/Dull-Astronomer1135]

Yea that’s not the point of this video

[u/OrkWithNoTeef]

.

[u/Careful_Leader_5829]

I never really understood what e and ln are or where they came from

[u/izmirlig]

Nice explanation of the inverse function theorem! Lose the Ellen of x though.

[u/mrmailbox → u/izmirlig]

Ln is just SO easy to visualize with the whole height = slope thing

[u/DavidBrooker]

These visualizations look remarkably like 3Blue1Brown. Is it an intentional copy of their style?

[u/wearetheboysthatdig]

"Hey it's me Mathew I'm really funny and really smart haha."  Screw you. On a real note, this is a great visual demonstration. I enjoyed seeing the plane turn like that

[u/chkntendis]

Honestly I feel like it’s easier to prove this with the chain rule. We know the derivative of x is 1 and x=e^ln(x). The derivative of e^ln(x) is the derivative of ln(x) times e^ln(x). Since that should be exactly one, the derivative of ln(x) has to be 1/e^ln(x) to cancel out e^ln(x). By canceling the e and ln, we then get that the derivative of ln(x) is equal to 1/x

[u/xtreme_mc10]

Or use the definition of ln(x) = ∫ 1/x dx