Power Rule for Differentiation (3 of 4: Derivation of rule)

[@lewisrees756]

wow the power rule was never proven to me, I just took it as true and used it but you explained it clearly. thanks!

[@cable4751]

Watching through these calculus lessons everyday to get a head start on my year 12 calculus stuff, but mostly because I honestly enjoy your teaching. Thank you so much!

[@adityashastri5872]

ikr same here. I live in the US and am currently take AP Calculus, and I am literally the top in my class simply bc of Eddie Woo.

[@fisher00769]

Math education all over the world should be just this guy's videos. It would quickly become literally everyone's favourite subject (probably except for folks with math related learning disabilities).

[@quantumgaming9180]

I'm in 10th grade now but I just can't wait to start Calculus next year. You showed me a way to enjoy math 😀

[@shauryaagarwal4556]

Same!!

[@sheebashrivastava3042]

Aww man I am jealous of these guys whom you teach offline..

[@rmela4501]

What about when n is negative? Or not an integer.

[@ti84satact12]

It doesn't matter. The assumption is as long as 'n' is a real number the general formula that was proved will also hold. So this rule will also work for negative numbers and non integers.

[@rmela4501]

@@ti84satact12 what if n=pi? How would that proof work? Would (x^pi-c^pi) factor the same way?

[@elltwo8393]

TI84SATACT the theorem that is the so called “power rule” will indeed hold, but his proof falls apart. Difference of powers is not defined in the same way as for numbers that are not natural numbers. Furthermore, and even more gross example of how the proof falls apart is in the final step. Assume n=1/2. How can we add x^(1/2-1) 0.5 times? Again this proof is nowhere near rigorous enough to consider n in the reals.

[@theeligator8728]

wow i love this thank you so much. you are the best teacher

[@varunraju1569]

Which grade students are you teaching?

[@rubikashree7724]

my way of thanking him would be to watch all the ads completely haha

[@user-us4ws9px2s]

thanks, have not seen this proof before, really great explained

[@emiloberg2110]

I'm not going to learn calculus until this fall (school start 20 of august) but I'm looking forward to it. Your videos have given me a GOOD base knowledge and I can actually follow whats going on. Sadly I don't think my teacher will go this deep if I've known her right, but if she doesn't I can always watch this video! Thank you! Your videos have given me hope, I'm gonna try to get a higher grade in math this course, thank you for the inspiration! PS: You also have inspired me to become a teacher, I've never doubted what I wanted to be before I watched your videos. If i choose to study to a teacher I will probably be one in maths and science and would always strive to become as good as you!

[@sentinel_1752]

Emil Öberg hey my school starts at August 20th too and I’m also taking AP calculus

[@EpiCuber7]

"Yikers!" xD

[@mrgoat7988]

Wow! Great explication. Thanks.

[@Hepad_]

Still not a rigourous proof since you didn't really prove the identity a^n-b^n = (a-b)(a^(n-1)+a^(n-2)b+a^(n-3)b²+...+b^(n-1)), but that's enough for their level.

[@little_pro2162]

Everyone if you want to learn more maths check out Robert Muscatello

[@m_ko]

Nice way

[@elltwo8393]

This proof assumes n is a natural number. Proof falls apart otherwise (though it is true the conjecture holds for n in the reals).

[@sentinel_1752]

That’s insane bro

[@vaibhavvadoliya1641]

At the starting of this video Eddie says let f(x)=x to the power of n , but he writes f(n)=x to the power of n ; so don't get confused there , it's done by mistake

[@kyh148]

I think he wrote the x in a way that it looks a bit like an n

[@kyh148]

That's pretty cool

[@johnnolen8338]

Neat ... but it's only true when n is an integer. 🤔

[@adityashastri5872]

4:36 lol

[@razor1887]

wow