induction proof for the nth derivative of x*e^x

induction proof for the nth derivative of x*e^x #calculus

[ReconFX]

Oh hey, another video from whitedigitalpenreddigitalpen

[nicholasleclerc]

Dude, you’re the Bob Ross of calculus and math. X )

[eliavrad]

if you have xe^x=d/da(e^ax) when a=1, you can get the same answer without any induction. d^n/dx^n d/da e^ax = d/da d^n/dx^n e^ax = d/da a^ne^ax = (na^(n-1)+x)e^ax, when a=1 this is (n+x)e^x

[sweepingteyvat]

Dude, You saved my abstract algebra homework. Thank you!!!

[vitinho]

Hey! Happy bday BPRP! (and for ur gf)
We love your vids, and your way to explain things.
Ofc, if it wasn't you, I wouldn't be able to do calculus rn(I'm 15), you're my inspiration.

[MrRyanroberson]

In fact, it works for all integer n, and I would bet that noninteger derivatives would also apply (under typical rules) (just as the nth derivative of e^ax is a^n e^ax, it would most naturally work for all n) and might even go to complex numbers. But I won't go there just yet.

[notspaso]

I miss the whiteboard! I can't see your cool pen switch trick here! #SADYAY:(

[gergodenes]

Hey, I love these videos, and I have an interesting problem that has been on my mind for quiet some time now. Could you solve this?
What is f(x), where

[hibaabou]

Thank you very much !!! helped a lot !

[MiguelGonzalez-hysd]

Hey, blackpenredpen, could you prove that this funtion log x ((x^2)+(x^3)) when approaches infinity is 3? Thx

[hollow]

how about for the negative integers, is that the integration for the function?

[XanderGouws]

If you think of integration as a "negative derivative" the integral of y will be y^(-1) and it's easy to see that the integral of xe^x will be (x-1)e^x

[themeeman]

So would the dr peyam half derivative be (x+1/2) e^x

[jimmylu]

Hey man I really enjoy ur vids (they re literally lifesavers 😂😂)
It would be great if u could makes some vids about volumes of revolution b/c I'm struggling with this topic in school.
Thanks

[shacharh]

Here's another nice calculus question to be proven with induction:
Let P be a polynomial of degree n. Prove that the integral/antiderivative of P(x)e^x = Q(x)e^x + C where Q is also a polynomial of degree n.

Have fun with that one :-)

[henryh.]

Hey can you do the integral of sin(arccos(x)) dx from 0 to 1? And without any trig identity or trig substitution? If you want to know why I said that restriction, just graph the function. You will be surprised.

[destroctiveblade]

I mean there's the Leibniz formula for that right ?

[WilliamLeeSims]

Would this still be true for fractional derivatives?

[kaitiklee]

Why don't use Leibniz's theorem

[ssdd]

Happy birthday!






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