Finding the Total Differential of a Multivariate Function Example 1

Finding the Total Differential of a Multivariate Function Example 1

[redjr]

Thanks for the video man! It really made something click in my brain. For me, it was never the computation, but the notation that really confused me. Here's an explanation in hopes it helps someone.

Think of z as a function that takes in 2 arguments, called (x, y), and outputs some number. Given an input (x, y), the symbol dz is itself a *new* function that takes in two arguments, called (dx, dy), and outputs some number. What that number is is the best "linear approximation" of the difference of z evaluated at the original input (x, y), from z evaluated at the incremented input (x+dz, y+dy).

I would love some feedback and criticisms on this idea if anyone knows more about this than I do.

[thabisomatsena]

I've watched 10 plus videos so far and non of them made sense till this one, thank you very much!!!!

[wiredhead]

beautifully explained in less than 2 mins. i love you.

[hajorm.a]

you don't know what I was into before I watched your video, very simple and elegant.

[joesr]

Wait so we just leave the dx and dy there? Is there any way to get rid of it?

[souar]

So straight to the point. Really helpful!

[Fiedroz]

this guy just did 1h 30 minutes lecture in 1 minute 30 seconds... no every hero wear cape <3

[deathmate]

I am watching this during a final exam.
7 marks guranted now! yay!
Thanks to you of course!

[dicer]

Beautifully done! Simple, nice pace and wonderful example. Thank you for the help!

[susanwang]

Thank you so much! you made yourself so clear. I wish my lecture is half clear as you are.

[wjcbqcy]

Thank you for helping me.It's really a simple, wonderful explanation, and I got it in a minute and a half.

[corneliatomson]

Thank you very much!! That was very helpfull!! I could find an example of total differential anywhere

[misseducator]

thank you soooo much, very helpful video

[janvisagie]

Simple and efficient explanation, thanks

[jordanl]

haha you made it look simple, I like that

[chewy]

If you want to optimize the function how do you find dy/dx or it's reciprocal when dz is 0 and the equation is rearranged?

[stephenmontes]

what is the application of the total differential in calculus

[cheesedog]

Hello, I have a question, what if the variables has the same power? Like (x²)dx+(x²)dy?

[Hi-ombl]

what if its more than x and y? more than two variables?

[flame]

As great as the video was, can you please stop saying "del" for a partial derivative. I was woking along and got confused with vector calculus. :-p