Differentiability for Multivariable Functions

Welcome to my video series on Multivariable Differential Calculus. You can access the full playlist here:

Videos by Zack Cramer, University of Waterloo. Textbook reference: Essential Calculus by James Stewart

[arnavgupta]

Simply one of the best videos on differentiability of 3 functions with 3 variables.

[isharauditha]

the best explanation I have found on youtube about multivariable differentiation

[glaveglave]

Your video is easy to understand, simple, clear, detailed, overall excellent

[YonkoCraft]

Good simple and efficient i love it ♥️

[sohamghosh]

hi can you tell me if f(x, y)=xy/|x| (for x not equal to 0 and 0 elsewhere)is differentiable at (0, 0) or not, their partial derivatives do exist right?

[hallgatoandras]

The method from 10:40, doesn't apply to every function. For example f(x, y) = ((x^2)*y)/(x^2 + y^2) with this method I get that it is differentiable, but actually it's not. It is continuous in (0, 0) but not differentiable. Maybe I missed something.

[olivereinar]

I think the plane in the limit should be L(a, b) and not L(x, y), since you are measuring the distance between the image of (x, y), i.e. f(x, y), to the plane tangent to the point (a, b), i.e. L(a, b), as (x, y) approach (a, b).

[captainstreamer]

By Which Software You Draw Those 3d Structure ??

[dialgos]

This is wrong. A discontinous function CAN be differentiable in R^2. Atleast that proof is an exercise in my class right now