I've always wanted a proof of this since high school! I'm 29 now and you made my wish come true finally :D
@MrRyanroberson14 жыл бұрын
2:20: for g(a) = c, we apply the product rule and get (fg)'(a) = f'(a) c + f(a) 0, as long as f is not infinity then this results in a trivial expression cf'(a)
@MadScientist06234 жыл бұрын
Thank you for this. I wish I had this 5, if not 10 years ago. I find that most Calculus textbooks define the concept of a limit, show a few examples and then go over derivatives and then stop explicitly linking the two again. It then tends to be found at the beginning of integration and the same story occurs. I think that more should be shown with limits as they really are the foundation that Calculus is based off of.
@TheMauror224 жыл бұрын
Cool, suddenly the derivative rules become so easy and understandable
@punditgi4 жыл бұрын
For the chain rule if f(x) = f(a) for some neighborhood of a, then the proof fails because of division by zero
@jadegrace13124 жыл бұрын
I don't think that's true because if you use f(x)=x then the proof works fine if you follow the same steps
@punditgi4 жыл бұрын
@@jadegrace1312 But other functions could be constant over some interval around a. This is a well known flaw on the proof as presented, which otherwise is very nicely done.
@jadegrace13124 жыл бұрын
@@punditgi That makes sense. Very interesting.
@punditgi4 жыл бұрын
@@jadegrace1312 The problem is that the totally correct proof is a little more complicated in order to avoid that division. I hope our presenter shows us the revised proof with his usual clarity. 😃
@stephenbeck72224 жыл бұрын
There’s nothing wrong with the proof. Every derivative definition has a “divide by zero”. But this division is inside a limit in an indeterminate form ( 0 / 0), so we can use limit properties to evaluate the limit.
@goodplacetostop29734 жыл бұрын
14:21
@jaskarnd59934 жыл бұрын
That’s a good place to stop
@pbj41844 жыл бұрын
When will you do the AMA?
@revoltoff4 жыл бұрын
I am struggling here with finding derivates in points of the inverse functions and this guy makes this all look so easy LOL
@M79RS4 жыл бұрын
May not have been a good idea to use a as your variable of choice here
@borisbryant.0074 жыл бұрын
mike i can't find the playlist on real analysis anymore .............. the main reason i became your virtual student
@CM63_France4 жыл бұрын
Hi, A rapid way for showing the derivative of the ratio. But may be we can exibit this from the product rule: We know that (fg)’ = f’g+fg’, that tells us that f’g = (fg)’ - fg’, and then f’ = ((fg)’ - fg’ )/g . Let u = fg, then f = u/g, and then (u/g)’ = (u’ - ug’/g)/g . Let’s multiply up and down by g : (u/g)’ = ( u’g-ug’)/g² For fun: 1 "and so on and so forth", 12 "go ahead and ...", including 9 "let's go ahead and ...", inluding 2 "let's go ahead and do that", 6 "great", and the usual "and that's a good place to stop".
@revoltoff4 жыл бұрын
Finally something I can understand lol. Taking a Calc 1 type of class with stat for my BA bSc which has kind of nothing to do with math in my opinion but hey, they force you to take it to ''show your brain cells are working'' from my understanding lol... But I like to watch these cool math videos to understand better and hopefully pass my exam
@tomatrix75253 жыл бұрын
Best of luck. Don’t get overly taken up with real analysis...It’s a bit much for only calc one but definitely watch if genuinely interested.
@samkirkiles67473 жыл бұрын
Could you explain the compositional limit part at 8:51?
@tomatrix75253 жыл бұрын
Lim x->a f(x)=f(a) is something basic that you probably know given f cont. at a. Looking at his original definition of g’(f(a)) involving y, it uses lim y -> f(a). We can replace the y with anything and adjust the lim something -> something else once the y placeholder still approaches f(a). Therefore, if he replaces y with f(x), and we know lim x-> a f(x) = f(a) , thus that lim something -> something else is lim x-> a, so then the y placeholder (which is f(x)) becomes f(a) as required. I might even be ‘over’ explaining this as it’s really a simple property of limits, but I suspect you’re overthinking it or getting confused among the rest of the contents of the video. Hope it helps.
@anakinkylo.thepomenerianan90843 жыл бұрын
this course style reminds me of rod haggarty textbook
@anakinkylo.thepomenerianan90843 жыл бұрын
excellent stuff the way you teach most people skip his stuff cause they confused but you convey it an excellent manor
@TechToppers4 жыл бұрын
Let s(n) denote the sum of the digits of a positive integer n in base 10. If s(m) = 20 and s(33m) = 120, what is the value of s(3m)? Can someone please help me with this? It came in India. PRMO 2019 25th August Paper
@arvindsrinivasan4244 жыл бұрын
🔥🔥🔥
@jaskarnd59934 жыл бұрын
Im having trouble with this problem can you please help me. Find the function f(a(g)) where a(69) = 80085 and f(420) = 911
@revoltoff4 жыл бұрын
I would start by trying to roll the function up into smaller bits maybe and then trying to see if there is any element you can apply in order to give some sort of an equation to the problems... hopeit helps
@minh95454 жыл бұрын
Why does this function look like a joke?
@minh95454 жыл бұрын
Oh shit, it is
@jakimoretti77714 жыл бұрын
here is a vid that might help! ;) kzbin.info/www/bejne/bJDFaIV6qrGqmas
@tgx35294 жыл бұрын
for example [(80085/69)*x]^k=911, there is k=ln 911/ln(80085*420/69), (we take the linear function only for x>0, there exists ln function)