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

I discuss and solve an example where we calculate the partial derivative of $\arctan (y/x)$ with respect to $x$. The method of solution involves an application of the chain rule. Such an example is seen in 1st and 2nd year university mathematics.

Category:

Education

Tags:

• partial
• derivative
• chain
• rule
• mathematics
• calculus
• MATH2019
• Chris
• Tisdell
• UNSW
• multivariable
• tan
• inverse

[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.

[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!

[krqgrk32]

wow clear and thorough~~ simply wonderful~

[00Lawless00]

This is very clear and made simple. Cheers.

[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!