Second Derivatives Using The Multivariable Chain Rule

We show show to use the Chain Rule twice in a row. This will require the use of the Product Rule and Chain Rule.
#mikedabkowski, #mikethemathematician, #profdabkowski, #calc3

[@CharlesChow-en2zc]

Thank you sir, best explanation I've came across

[@mikethemathematician]

@CharlesChow-en2zc Thank you so much!

[@darrenpeck156]

Excellent video

[@mikethemathematician]

@darrenpeck156 Thanks so much!

[@gargikaushik7621]

best explanation

[@mikethemathematician]

@gargikaushik7621 Thanks so much! This is a tricky topic! See this video for some of the complexity in the matter:
czcams.com/video/N7D61Mp4QqI/video.html

[@ejimadam2022]

For the portions of the equation where you've highlighted that the chain rule is to be used. Why are you differentiating the x and y derivative of the expression you have for dw/ds instead of what's in the boxes?