Real Analysis Ep 31: The Chain Rule, etc

[@tribima1698]

when we define d(y), we have g'(f(c) is limit of y goes to f(c) .... How about at the and of proof, when we take limit x goes to c (after we div. by (x-c)), what the reason we can get lim x goes to c of d(f(x)) is equal g'(f(c))? g'(f(c)) in the begining we have limit y goes to f(c) and the end of proof we take limit x goes to c and we have also g'(f(c)), I missed something in this part.. thank you very much for the explanation...

[@valeriereid2337]

This is why I love mathematics - it is legit!

[@emmazeng2395]

I don't really get why d(y) is continuous when it equals to g'(f(c)). Last class we have an example that f is continuous but f' is not, right? Then why can we say g' is continuous here?

[@ChrisStaecker]

You are right that g' may not be continuous! But d(y) is not equal to g'(f(c)), we only know that the limit of d(y) at one point equals g'(f(c)). The definition of d(y) at 19:50 shows that it's just a sum/quotient of other continuous functions, so d(y) will be continuous as long as y≠f(c), and I explain around 21:00 how we can make it continuous at y=f(c) by patching the domain at that one point.

[@jphili]

Hey Chris I love your channel and have a lot of the same math gadgets you do. Curious... have you ever looked into slide rules? You seem like a guy who would be into those.I have a few. Faber Castell 2/83n, versalog and a few other classics. Another thing I dedicated about a year of my life to researching is the 60 minutes stopwatch from the tv show 60 minutes. I fiiiiiiinally figured out what the original model was and picked one up on ebay. Also mechanical...

[@ChrisStaecker]

Thanks! I have a few slide rules, but I'm not a true expert. Actually one will make a brief appearance in my next video...

[@hunterroy8485]

That speed limit thing sounds like something a physicist made up......