Proof: The derivative of __ is __ | Advanced derivatives | AP Calculus AB | Khan Academy

Proving that the derivative of __ is __ using the definition of the derivative as a limit, and the definition of _ as a limit.

AP Calculus AB on Khan Academy: Bill Scott uses Khan Academy to teach AP Calculus at Phillips Academy in Andover, Massachusetts, and heÕs part of the teaching team that helped develop Khan AcademyÕs AP lessons. Phillips Academy was one of the first schools to teach AP nearly 60 years ago.

For free. For everyone. Forever. #YouCanLearnAnything

[TheHalawaniTube]

"Who has not been amazed to learn that the function y = ex, like a phoenix rising from its own ashes, is its own derivative?" - Francois le Lionnais

[sharonsolana]

Thanks for not skipping steps Sal! : )

[cienciandre]

Finally someone who doesn't skip the resolution of the limit or use d(lnx)/dx to prove it

[always-alicia]

Okay... that was the best thing I’ve seen all night! Very well done!

[icanmakemusic]

at 7:15 you change the ln((1+n)^(1/n)) to the ln of the limit of ((1+n)^(1/n)). What property is that?

[MPierce]

Dear Khan, I love this video so much. Your passion for teaching just shines in how amazingly you explained this beautiful phenomenon of the number e. God bless you for being a great teacher!!! =)

[catorlife]

wait? at 0:23 why e=lim(1+n)^1/n when n approaches 0??? i haven't seen that definition in anywhere?

[andrexeme_swag]

What an elegant proof! I'd like to ask just one thing: from 1:07 to 1:19, wouldn't the slope of the tangent line be equal to "exp x" instead of just "x"?
I also might have misheard something, so any clarifications would be appreciated :)

[charlottaatlas]

😂😮😅😊you cant do what I can unless I teach you and I wont😢 that you😅thats me Bye🎉your heads

[andreapaps]

Great proof its so simple and yet rigorous enough :D

[hasanburney]

WHY DIDN'T YOU POST THIS 3 DAYS AGO?!?!
Still great video and thanks

[JohnSmith-one]

why is 'e' defined in such a way? where does this definition came from?

[timding]

At 2:52, I do not understand why the e to the power of x is moved to the front of the whole limit. Many videos say the same thing but never explain that. Is there a video that explains that? Thank you!

[michellauzon]

What about Exp(x) = Limit on n of S(x, n), where S(x, n) = Summation from 0 to n of x**k/k!. Because S(x, n) converges uniformly on any finite interval, we can do the derivative before the limit. And because d(S(x, n)/dx = S(n-1, x), the limit of the derivative is the same than the original limit.

Lim S(n, x) can be the definition of e**x

[atulmathur]

Your explanation is really good but your English is great ! For me, that makes all the difference .

[Pancake]

great improvements in these introductory differential calculus videos :)
keep it up!

[zaidhamdaan]

Thank you so much sir, awesome video finally I was able learnt it alhamdulillah

[diya]

Thankyou so much sir! It all makes sense now..

[mandeepprajapati]

Please solve e^x^2 with first principle

[nbme-answers]

Title of this video is: Proof: The derivative of 𝑒ˣ is 𝑒ˣ