Chain Rule Challenge

Challenging Chain Rule Problems

In this video, I provide some more challenging chain rule problems. Are you ready for the challenge?

[yakirkaye]

I finally realised what that chen lu is, lmao

[Kdd]

Plz do a QNA anytime soon!!
Love from India😊😊😊

[DOCTORCola]

*I love this channel! ))) I wish you to become famous all over the world as soon as possible!*

[loopgaming]

when I saw this video on my right panel I was literally jumping with joy!!!!

[easymathematik]

One could try it via recursion:

f(x) = xe^-x
f ' (x) = e^-x - xe^-x = e^-x - f(x)

Another way is using binomial theorem for derivatives.

That should give the answer immediately, because d^k x/dx^k = 0 for k > 1.

[PokeMC]

Thank you very much, Dr. Peyam! A wonderful video to wake the brain up in the morning.

[stefanocarini]

You're a formidable teacher! Greetings from Italy
P.S. Go Chen Lu, go!

[MrNerst]

So the prototype condensate formula is: that includes f(x)=f^0(x)=x*e^(-x). The next step is to prove it by induction, one needs to derive again with respect to x, obtaining: [f^(n+1)](x)=[(-1)^(n+1)]*(x-(n+1))*e^(-x), et voila! The formule is valid for every natural number n, therefore, you can continue and safely compute the 1000th derivative.

[Khalid_]

My tacher thank you so much ❤️
❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️I happy to watched this video
It was useful for me

[shivarammani]

Wow... Was very useful.
Chen lu for the win!!!

[neilgerace]

10:20 Why don't we use degrees? Because we are all adults now!

-- blackpenredpen

[ogorangeduck]

1:00 But brute forcing is how I attempted to solve an AIME problem last year!

[Math]

For the first challenge (the 1000th derivative of xe^x): I have ever thought about it before, but you explain the thought here very clearly in your videos. Thank you very much for the explanation 😊. It seems that you like to learn about "infinity things" hahaha....

[prateekmourya]

Is there any solution to x+y'=y+x' or x+x'=y+y'

[szerszen]

Lovely definition of derivative by Ex. 6 <3

[Armbrust]

The first one could be easily proved with mathematical induction.

[nahweh]

The first problem would have made a sweet intro to proof by induction. (Missed opportunity?)
Problem #5, too, would provide a nice example.


You forgot the cool derivative of an inverse function! (IMHO, of course)

[benjaminbrady]

Are you back in the classroom? I hope you're safe if you are