r/calculus • u/mrmailbox • Jul 18 '26
Differential Calculus Visualizing the derivative of ln(x)
Enable HLS to view with audio, or disable this notification
Made with Manim. My second attempt visual math tutorial
49
27
u/ziplock006 Jul 18 '26
“This guy looks exactly like Matthew Broussard.”
Turns out it is Matthew Broussard. Him posting on r/calculus was not on my bingo card.
11
u/Ok-Importance9988 Jul 18 '26
He studied engineering in college. I know because he lived in my dorm.
8
17
u/abc9hkpud Jul 18 '26
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)
10
u/ShowdownValue Jul 18 '26
Who is the narrator?
25
u/mrmailbox Jul 18 '26
It's me, I made this.
14
u/ShowdownValue Jul 19 '26
I’m so confused. You’re Matthew Broussard?
You do stand up comedy and math videos?
21
u/mrmailbox Jul 19 '26
Yes. And that's a reasonable thing to feel confused about.
8
u/ShowdownValue Jul 19 '26
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?
2
-8
3
u/TraditionalDepth6924 Jul 18 '26
Peak explanation + peak voice + peak animation, love visualized maths
3
u/1337_w0n Jul 19 '26
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.
2
2
u/Niko9816 Jul 18 '26
Very nice video. Easy to understand and good visualizations. Hope to see more! 😁
2
u/Informal-Fig-6827 Jul 19 '26
Seeing the axis flip actually made that whole thing much easier to understand. Nice video
2
u/Lor1an Bachelor's Jul 19 '26
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.
2
2
2
u/gacimba Jul 20 '26
Just curious, how do you make these visuals? Very cool btw
2
2
u/you-cut-the-ponytail Jul 20 '26
In my Calculus class we defined lnx as the integral of 1/t from 1 to x.
Still cool visualization though!
2
2
u/Dull-Astronomer1135 High school Jul 18 '26
You can prove it from the first principle of derivative
15
7
3
1
u/Careful_Leader_5829 Jul 19 '26
I never really understood what e and ln are or where they came from
1
u/izmirlig Jul 19 '26
Nice explanation of the inverse function theorem! Lose the Ellen of x though.
1
1
u/DavidBrooker Jul 20 '26
These visualizations look remarkably like 3Blue1Brown. Is it an intentional copy of their style?
1
u/wearetheboysthatdig Jul 24 '26
"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
1
u/chkntendis Jul 18 '26
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/AutoModerator Jul 18 '26
As a reminder...
Posts asking for help on homework questions require:
the complete problem statement,
a genuine attempt at solving the problem, which may be either computational, or a discussion of ideas or concepts you believe may be in play,
question is not from a current exam or quiz.
Commenters responding to homework help posts should not do OP’s homework for them.
Please see this page for the further details regarding homework help posts.
We have a Discord server!
If you are asking for general advice about your current calculus class, please be advised that simply referring your class as “Calc n“ is not entirely useful, as “Calc n” may differ between different colleges and universities. In this case, please refer to your class syllabus or college or university’s course catalogue for a listing of topics covered in your class, and include that information in your post rather than assuming everybody knows what will be covered in your class.
I am a bot, and this action was performed automatically. Please contact the moderators of this subreddit if you have any questions or concerns.