Derivative of ln (x) using the definition of derivative

[@WolfgangFeist]

Second last step: you need to use "continuity" of ln(x). (Because:with still finite x/h the term in the ln is not yet 'e'). BTW: I love the way you are presenting this explaining every step (in a calm and friendly way). Most teachers try to do it in a hurry. That is the main reason, why some students get annoyed with math.

[@AvneeshKumar-x4o]

And in the limit the variable should approach infinity

[@temporarychannel9759]

the enthusiasm made this really enjoyable to watch, great job

[@averagestudent5222]

This guy turns math into magic

[@SpiroGirah]

I never thought of this! Good job!

[@barthennin6088]

Beautiful! 1st time seeing this truly from first principles!

[@boguslawszostak1784]

If you define ln(x) as the integral from 1 to x of 1/u du, you have no problems computing its derivative. It is equal to 1/x by definition of the function.

[@Th3OneWhoWaits]

8:58 as h goes to 0, "n" or x/h goes to infinity. Thus, lim as h goes to 0 = lim n goes to infinity.

[@manoharkanade7383]

Very good explanation ❤

[@ecSruthipriyaMahesh]

I really like your classes, thank you for your hard work! 😃

[@sldw3221]

Hello sir, i'm seeing that we always using definition of e with limit while proving all of these formulas but is it actually possible for you to explain or prove how or why limit n->infinity (1+1/n)^n is equal to euler's number? Did you record a video about this or would you talk about that in another video if it's possible? Thanks

[@wira2562]

It's very useful to understand the inderivatived integral of dx/x sir!

[@robertveith6383]

Use grouping symbols: (dx)/x

[@Harrykesh630]

just a suggestion 😁 It might be too late to point out but, you could have started by first proving that ln(x) is indeed differentiable by Left and Right hand derivative then go on to find it.

[@nellwackwitz]

You are AWESOME!!

[@AvneeshKumar-x4o]

But the variable should approach infinity

[@nichodimuszishiritinashe8329]

You are the best

[@surendrakverma555]

Very good. Thanks 👍

[@alexdcruz3682]

Love your videos

[@EternalScienceAndTech]

You are a great man

[@samwelkariuki3114]

Always the best teacher.....what about 1/x

[@PrimeNewtons]

Thanks

[@elai3147]

5:31, as h goes to zero wouldn't x/h go to either positive infinity or negative infinity?

[@xavierwainwright8799]

This works because lim x-> -inf (1+1/x)^x is also equal to e, but I don't know any proofs without using the derivative of ln(x) (this would be circular reasoning).

[@cblpu5575]

Recall that the domain of ln (x) is **positive real numbers only** hence x/h is a positive real number x divided by a quantity h tending to zero

[@wilsonhicke5598]

Love this

[@EliiiAkotha]

Great job

[@salamalmudarris5032]

But n is integer while x/h is real number?

[@sandraboateng5435]

😍😍👌👌✊✊👍👍

[@januszek1760]

(1 + 1/(x/h))^(x/h) is not equal e

[@Artemis1855-k4w]

as h approaches 0, x over h approaches infinity, if you replace x/h with a variable it's more legible

[@festusemmanuel2111]

Wow ❤

[@hassanejturay2994]

Awesome

[@katiatzo]

BRAVO

[@holyshit922]

He missed step when he used fact that ln is continuous

[@joelmwape4239]

You are the best

[@PrimeNewtons]

Thank you for your kind words.