Proof: Derivative of ln(x) = 1/x by First Principles

In this video, we prove a fascinating result that d/dx[ ln(x) ] = 1/x by the definition of the derivative, First Principles, and by the definition of the number e.

#calculus #derivatives #logarithm

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Please ask me a maths question by commenting below and I will try to help you in future videos.

[danjaboy]

This channel deserves way more attention. That was such a long proof yet so easy to understand from start to finish. One of those YouTube videos teachers will show students because it's better than their own explanation.

[kiddsavage]

3 years later and this is still helping people, this video helped me understand this limit after watching multiple videos and not understanding, Wish more growth to your channel. hope my sub will be the start of many more.

[edwardgraham]

Can't see this too many times --- thank you for the nice reminder!

[thedeathofbirth]

Excellent communication skills! Thank you for the time you took to make this video!

[mdabirkhan]

sir you fulfill my desire. I also saw many video in many channels but did not understand anything. Best luck for your future

[atishghosh]

Great explanation—instant like and subscribe!

[ThuyTrucPham-mtzq]

Awesome
You make it so easy more than my teacher does
Tks for this

[scientistwannabe_]

I do it with lim[(lnx-lnx0)/x-x0]
x->x0. becomes limln(x/x0)/(x-x0)
x->x0
Then i pose u=x/x0 and the limits becomes
lim lnu/[x0(1-u)]
that lim(lnu)/(u-1)=1 using N-L theorem and squezze theorem
u->1

[dekeltal]

Can anyone explain why in 5:25 you can take the 1/x out of the limit, saying it's "independent of the letter m" - after all m is defined as a function of x?

[mdabirkhan]

dear sir some point you didn't clear it is very difficult to understand for beginners. like you didn't clear from where n and m had been come . I hope you will reply my comment and help me to understand this

[Hanan-eokk]

Great video. But where did you get the formula for e from?? 1:06

[knib]

Did you need the defn of e?? Your last limit (1+1/n)^n as n approaches infinity is 1, no?

[kjfjqrl]

At 6:08, how do we account for m<0? Using my calculator, it seems that n -> -infinity has the same result as n -> + infinity, but is there a way to prove this?

[BilalAhmed-onkd]

why did i move 1/x outside the limit of m, when it is actually an expression in terms of m

[samarjyoti-ray]

you didn't explain why we can take the limit inside the square bracket.

[timm]

you can prove this in four steps using implicit differentiation and definition of natural logarithm.

[weinsterle]

This proof is incomplete, since you did not show that the limit as n aproaches infinity of (1+1/n)^n = e but just took that for granted. It is not obvious that this limit converges in the first place, since lim n->infinity [f(n)]^[g(n)], where lim n -> infinity f(n) = 1 and lim n -> infinity g(n) = infinity is an indeterminate form.

[ashmain]

I know this is a late comment, but a lot of the algebra in this video is unclear, at least to me, it does not seem to be "first principles" as described.

[ammoursidicharef]

Par définition le logarithme est la primitive de 1/x

[SuperYoonHo]

THANKS SO MUCH I SUBSCRIBED PLEASE REPLY SIR!!!