Multivariable Calculus 5 | Total Derivative

[@LucasDimoveo]

I just found out about the Total Derivative from wikipedia a few hours ago. My mind is completely blown!

[@mastershooter64]

the total derivative! the most general derivative in multivariable calc!

[@ahmedamr5265]

Thanks for the great video!
I hear people refer to df_x sometimes as an exact differential. Would you have any comment on this?

[@brightsideofmaths]

Thanks! This is discussed in the manifold series :) See here: tbsom.de/s/mf

[@IzauroNeto]

infinity ♾️ ∞

[@henkolsonpietersen2242]

I love you for this! My professor writes the material we use and his explanation are very, VERY succinct.

[@brightsideofmaths]

Nice :) And thanks for the support!

[@henkolsonpietersen2242]

@@brightsideofmaths I promise that once I'm no longer a broke student, I will support you financially

[@brightsideofmaths]

@@henkolsonpietersen2242 Thank you very much :)

[@AJ-et3vf]

Great video! Thank you!

[@Elektrolite111]

Great video, thank you

[@brightsideofmaths]

Glad you liked it! And thanks for the support :)

[@theoremofnik]

total tolles video

[@nayjer2576]

Why we can't just take the usual definition, f'(x) = lim h->0 f(x+h)-f(x) / h ?

[@brightsideofmaths]

How to divide the vector h?

[@nayjer2576]

@@brightsideofmaths II h II *

[@brightsideofmaths]

@@nayjer2576 So what is the difference to the video then?

[@nayjer2576]

@@brightsideofmaths Is the problem that we have multiple directions for the vector h and each differential could be different? That would be the idea of the directional derivative, right?

[@brightsideofmaths]

@@nayjer2576 Yes, the total derivative has to cover all directions.

[@plegasus7308]

What’s is your opinion of Amann and Escher analysis series?