Proof of the derivative of lnx: A Step-by-Step Proof and Explanation

[@akrammohamed8374]

Never thought I’d learn maths from Arnold Schwarzenegger

[@mathwithalex]

Stay tuned. I'll be BACK!

[@winonamama8358]

boy what are you saying

[@mtaur4113]

Needs more parentheses to be totally clear on the log rules. Maybe even square brackets at some point to get out of nestsd parentheses hell. Implied parentheses for ln x^p is kind of slippery, especially when writing ln(x^a)^b to mean ln( [x^a]^b ) when it looks more like [ln(x^a)]^b.

[@mathwithalex]

I see. There could be some confusion. Thank you for pointing that out.

[@curiousaboutscience]

That is pretty cool to see worked out!

[@mathwithalex]

I appreciate your ongoing support. I'm enjoying watching the videos you upload as well!

[@mathwithalex]

For the exciting proof of the Euler number used in the video, take a dive into the rabbit hole through this link: www.youtube.com/@mathwithalex/community Your curiosity is appreciated!

[@Jan_Heckmann]

Hello there! I see that you proved that e=lim x->0 of (1+x)^1/X three different ways. But is it true, that only the second prove counts? Because the others use the derivative of the natural log, leading to a circular reasoning.

[@Nzargnalphabet]

I’ve actually always preferred the infinitesimal definition of derivative, it makes more sense and you can kind of just plug and chug, but limits are cool too I guess

[@mathwithalex]

Thank you for watching. Please feel free to leave your opinions in the future as well. Thank you.

[@davannaleah]

How about: y = ln(x) So x = e^x dx/dy = e^x which is x So dy/dx = 1/x

[@mathwithalex]

You're referring to "x=e^y," right? It's a quick and convenient approach! Thank you for the great feedback. Please continue to share your valuable insights in the future.

[@davannaleah]

@@mathwithalex Ah, yes, sorry... mistype

[@mathwithalex]

No problem at all. I make typos too often. I wrote it down so that others can see and understand. Thank you.

[@MH-sf6jz]

Have you proven the inverse function theorem?

[@mathwithalex]

I apologize, but the video explaining the proof of the inverse function theorem is not yet prepared. I will add it to the upcoming video list. Thank you for your valuable suggestion.

[@nicolascamargo8339]

Saludos desde Colombia

[@mathwithalex]

Hola. Gracias. Saludos desde un coreano que vive en Singapur.

[@nicolascamargo8339]

Wow excelente

[@mathwithalex]

Voy a seguir viéndote en futuros videos, esperando siempre contenido excelente.

[@mndtr0]

(lnx)' = ln 😅

[@mathwithalex]

haha~ 😄

[@sigmascrub]

This gave me a chuckle 😂

[@mndtr0]

@@sigmascrubI'm glad that you have fun ^^

[@adrified9352]

Funny joke

[@loich.9133]

ln(x) is not a function, therfore you can't write (ln(x))'. ln is the function, you must write with this notation ln'(x). It's like f(x). You write f'(x), not (f(x))'

[@samueldeandrade8535]

Shut up.

[@TranquilSeaOfMath]

Very nice. Done like the pro you are. 🧮 Cheerful Calculations!

[@mathwithalex]

Glad you liked it!