Big picture of Total Differential and Chain Rule

You might have heard that total differential means
how much you go up on a mountain.
Would you like to know the reason?

You might have differentiated by using the chain rule
at an exam in the university.
Why can we differentiate like that?
Do you have a clear image on chain rule?

If you have these questions, this video will help you.

[gallonsofwater]

Had to sit down and think for a good 20 minutes just to get what you were saying about total differentiation... I will confirm, one of the most unexpectedly climactic moments ever, thanks for the video Sir!

[hoho_jeong]

Now I understand what I taught in class yesterday! Thank you so much.

[bradleygaddis]

Wow, ...clears up so much confusion!!!
Keep up the good work!!!
Thank you!!!

[krutarthparikh]

Thank you so much for explaining in this way. That actually helps understanding what exactly the end result of a TD means.

[gauravbharwan]

You have the potential to be best maths channel

[ahmedalmuhanna]

Thank you! You made everything clear. Hope to see more video like this!

[pedrocolangelo]

Thank you so much for such a valuable video. By the way, your choice for the soundtrack was amazing, it somehow makes it easier to understanding by making us less anxious when watching it, lol.

[vincentchong]

Thanks for your eye opening explanation. I wish you have more videos or books on this. btw, is there a typo in 9:37? in vide d(f(x, y))/d(t) = ... + (d()/dY)*(dX/dt), should be (d()/dY)*(dY/dt)?

[TJ-hsqm]

At 0:14 in the video, he divides both sides by DT. I wonder why the second term after the plus sign is df/dy*DX/DT instead of df/dy*DY/DT.
...this is clearly a mistake and the second term should be df/dy*DY/DT !!!

[mroseleiyud]

Thank You so much for this! Could you also explain approximating the tangent plane by total differential?

[mrslave]

9:28 "if the parameter t moves a little" - we cannot see t in this diagram. t is the time (for example). it does not move. it ticks.

[mrslave]

10:02 "if t goes up by 1 meter" - i'm convinced the narrator does not understand the chain rule.

[nicksm]

Oh god, why did you put this stupid music here? It's very distracting.