Chain rule: partial derivative of $\arctan (y/x)$ w.r.t. $x$

[Gearzish]

thank you very much! i wish proffs in my uni would teach your great diagram.

[DrChrisTisdell]

@Gearzish You might like to show your Prof if they are unaware of the diagram. Certainly helps from a computational point of view.

[smithsansoo]

Excellent! So much was made clear! Thank you!

[DarkChii77]

oh wow!!! thank you!! :)

that was a very clear, step-by-step explanation. just what's needed.

[floyd617]

THANKS YOU SOOOOOOOOO MUCH FOR THIS.... I UNDERSTOOD EVERYTHING YOU SAID AND I ACTUALLY UNDERSTAND THE CONCEPT NOW!! I WAS STUCK ON A QUESTION AT HOME AND THANKS TO YOU I FINALLY FIGURED IT OUT.. THANKS SO MUCH AGAIN

[domhedouin]

thanks a lot for this video, I am studying Calculus 2 at Southampton University, makes so much more sense when I saw you work through it!

[DrChrisTisdell]

@870rahu /watch?v=cm4N04A-G8U for some Taylor and Maclaurin series. Enjoy!

[cooroxd123]

hello, do you have videos on high order partial derivatives involving chain rules?

[hb8secs]

thanks alot that makes sense finally!! i wanna become math professor one day...cuz its so complicated initt...thanks alot

[additionse]

thx!

[Judomannen2]

Very good! Saved my evening :)

[pikla407]

Thanks a lot. I am currently studying Mathematics for Engineers at University of Malta and this video really helps =)

[hannahclaire42]

thanks, been struggling with multivariable calc, this really helped clear the chain rule up.

[TheHeatherMae]

Is there anyway you'd do an example with something like

Let w = cos(x-y)

x = t^2

y = sin t

This one confuses the heck out of me

[mechwarreir2]

Thanks man! Im not taking calculus at all yet, but im studing it in advance, thanks for the advice!

[netninja90]

Hi Dr. Tisdell!

Thank you very much for this example. I am currently studying Calculus 2 in Melbourne and this helped me a lot. Thanks once again.

[DrChrisTisdell]

You're welcome!

[pigeon7777]

@netninja90 LOL WTF me to! Melbourne uni? Parkvile?

thanks it helped me a lot to!

[netninja90]

@pigeon7777

Yeah Parkville haha. Youtube is awesome.

[pigeon7777]

@netninja90

LOL if i know u in real life

Im matt turner know me?

[TroyaE117]

It is not necessary to use subsitutions

This one will work...

Allow z = Atan{y/x}.

What is needed is dz/dx

Take Tan of both sides...

Tan{z} = y/x

Make x the subject...

x = y*cot{z}= y*cos{z}/sin{z}

continued...

[shadowC10ne]

Great!

[headspung]

soooooooo helpful, thanks!

[omiejay]

blah blah blah 1231 blah blah

[DrChrisTisdell]

Hi Caz - did you also use the chain rule to calculate $\partial w / \partial y$? If so then you're on the right track. (You should get $\frac{-y}{x^2 + y^2}$.)

To get the 2nd-order partial derivatives, the chain rule is no longer required. It's just a matter of taking the derivative and keeping the other variable fixed. You should get: $\partial^2 w / \partial^2 x = \frac{2xy}{(x^2 + y^2)^2}$ and

$\partial^2 w / \partial^2 y = \frac{-2xy}{(x^2 + y^2)^2}$.

Hope this helps!

C

[203132]

he sounds like the guy on australian top gear

[nogigglingmajor]

I love this lighting discussion; Do I sense a major Chris Tisdell 2019 movie coming? *laughs*

BTW, you do so many accents in class that make us all laugh and actually want to go to lectures....you should do this in you videos too...it makes maths funny!

[DrChrisTisdell]

I'm glad that you want to come to class - even if only for entertainment!

Funny you should mention movies...... I start filming of full-length lectures next week (MATH2111). All I can say is that I hope there's a good make-up artist about because I need all the help I can get!?!

[patricksaid]

Hey Dr Chris,

Even though you can sound just the smallest bit crazy at times, the way you ask yousrself a question from the humble students' point of view, and then answer yourself in a logical, easy-to-follow method is really good. It makes this maths much easier to digest. These videos are really helpful too!

[DrChrisTisdell]

Haha!! Being a little crazy comes with the job, Patrick!

Good to know I'm getting a good feel for what's on your mind!

[VegetableBun]

hey lecturer...your video are very helpful..

some suggestion will be that

if you can use another style of question or different question from the lecture.. then im sure there will be plenty more people viewing the video.

thanks you

[DrChrisTisdell]

Thanks for commenting Veg! I agree with your comments. Thanks!

[ShuvK89]

Gday Dr. Chris, how've your holidays been? Just a note on that root 3 poem, the person who posted it was just copying it from a movie ((harold and kumar 2: escape from 2019), just in case you didnt know), wouldnt want that precious text book going to some faker right? hahaha

PS, all the videos go well, expect the lighting is a bit dull and your wardrobe could use a little work hahaha just kidding keep up the good work.

[DrChrisTisdell]

No problem, ShuvK!

You're right about the dull lighting. In the most recent vids I've experimented with post-production (like changing the brightness and hue) and seem to be on the right track!

[marzpop]

this is so helpful. I couldn't do it by myself, and maple spat out some crazy answer.

Thank You Tisdell

2019

[DrChrisTisdell]

Hey, no worries! Good luck with your class test next week.

[jshfrdm]

Im sure that I will always be A lonely number like root three The three is all thats good and right, Why must my three keep out of sight Beneath the vicious square root sign, I wish instead I were a nine For nine could thwart this evil trick, with just some quick arithmetic I know Ill never see the sun, as 1.7321 Such is my reality, a sad irrationality When hark! What is this I see, Another square root of a three

[DrChrisTisdell]

Wow - that is awesome!! Entertaining, witty and true.

[bOstik210]

so wise tisdell

repping the 2019

[DrChrisTisdell]

Good to hear you're enjoying this stuff.

[DrChrisTisdell]

Great to hear you're a grad student now. Keep up the good work!

[botjok]

Thanks Doc...

am now taking up graduate studies and it has been years since i have been using this..

you are of great help :)..

Very clear and direct....

Way to to go!!

[analyitic1]

great, nice one, your easy to understand. i just couldnt be botherd to look through my textbook. gotta love youtube

[DrChrisTisdell]

You're welcome!

[alanrtan]

I LOVE YOU CHRIS TISDELL!!!

[DrChrisTisdell]

Wow!....Now, that's enthusiasm! :-)

[DrChrisTisdell]

Thanks for commenting everyone!

Hope the videos are of some use. I'll be uploading more as time goes on..

[SteveFlynn0]

Hey Chris, nice initiative and a cool idea, I like that you have given us another medium to work with when we get stuck

[krqgrk32]

wow  clear and thorough~~ simply wonderful~

[DrChrisTisdell]

Glad you liked it!!

[00Lawless00]

This is very clear and made simple. Cheers.

[DrChrisTisdell]

Thanks!!