Proof of the Power Rule

I thought this was a fun proof :D

Product rule and Quotient rule proofs are coming soon.

Keep flexin' those brain muscles!

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[thedoublehelix]

Minor technical details: you can't take the log of a negative number so this proof breaks down there. Also the power rule isn't actually true for every real n. d/dx x^0 = 0/x which is 0 for almost all x, but is undefined at x=0.

[daisyg]

I'm almost offended that you don't have a lot more views. I hope you don't ever stop making videos, cause I'm starting on this math journey and videos like these save my life.

[victoraguiar]

You just blew my mind with the alternative proof. Thank you and God bless.

[kingwoomy]

Wow, I finished Calculus 3 last semester (thanks to God), and I was curious to know why the Power Rule works. I don't know the math behind the Binomial Theorem, but your first proof in this video seems so cool. It was SO satisfying to see that "h" in the denominator just go away.

[juliangavras]

I've seen the first method before, but I've never seen the second one. That was pretty cool.

[alkankondo]

Epic Math Time sent me here! Apparently he, you, and I all agree that we don't like to just be given formulas to blindly use, haha! I remember trying to use the Binomial Theorem to prove the Product Rule a while back, and I found it so satisfying to have all those terms with an h-factor zero-out, leaving me with the expression I wanted!

[suuuken]

You are really good at explaining! Really helped thanks a ton

[xjuhox]

Write x^n = x*x^(n-1) and use the product rule and induction.

[antoniogarcia]

As always great videos man. That Hendrix T-shirt is fire

[davemccleary]

Nice video. I'm going to assign my calc 1 students to watch it this weekend.

[skinnykevin]

Thank you so much! This was so interesting