Chain rule: 2nd derivatives example

Example on the chain rule for second order partial derivatives of multivariable functions.

[josevillalobos]

3:41 *walks away from projector for ten secons*
3:41 - 3:51 *hands continue waving around* awesome video

[InspirationIsFree]

Thanks so much - USYD student and this explained it so clearly. That little graph on the side helps so much with getting your head around the 2nd derivative.

[matthewbergeron]

saved my life thank you mr Australian man

[remixex]

Thanks you saved me, after 6 months of not studying this i tend to forget

[ahmedhashim]

Dr. hello I'm from your followers on YouTube has brought a lot of lessons you Thank you for your beautiful effort for the dissemination of science

[THSURVIVOR]

Thank you Doctor. Your way of writing the second deriative using the chain rule got through to me. I now understand perfectly.

[ThreeARKs]

This doesn't work for all problems. In the case of the problem that he discussed, Xr and Yr both only were functions in terms of theta. If you have different variables in Xr and Yr, you will have to deal with a product rule, usually with a term becoming zero because the partial derivatives would be zero.

[gustavodias]

Thank you! Thank you!!! Your approach on this matter is much easier and clear than most books and teachers. I'm fully grateful for your video =D

[nts]

Have you got a tutorial for finding d^2f/dtheta^2?

(This video was very helpful but I'm struggling to understand how to find the second order partial derivative of theta)

[MrMynd]

Thank you good sir. We use the same textbook at my University and I could not understand approach until I saw your explanation of it!

[stephberrie]

my book says something about doing product rule? is that necessary?

[DrChrisTisdell]

@9THSURVIVOR Great. The second derivative is the real challenge with these problems and I'm glad the diagram helped.

[akilakavisinghe]

Will this method always work no matter what?

[kushbur]

Why is theta treated as a constant when differentiating with respect to x or y? Isn't theta a function of x and y:  theta(x, y) ? Is x then treated as a constant when differentiating with respect to theta for instance?

[surajb]

Thank you so much. You solve my doubts about it

[ahmednouh]

please doctor if i wanna deriative w.r.t x instead of r what i should do

[mrtincz]

Thank you Dr. Tisdell. Very informative.

[bonbonpony]

04:34 When are they _not_ equal? I mean, when do the partial derivatives _not_ commute?

[username]

Excellent, we use the same textbook in my college.

[Raison_d-etre]

I wish you'd do an example where x sub r and y sub r are functions of r.