#yay I love how in one video, your topic is pretty advanced, and the next video you deal with something really basic, and you don't start saying "obviously" and talk down to your audience. You treat every topic like it is just as important as any other.
And the third way.... y = (3x+1)^(1/2) y^2 = 3x+1 derive 2y*dy/dx = 3 dy/dx = 3/(2y) dy/dx = 3/(2*(3x+1)^(1/2)) Personally I like the expanded form because then I can see if I missed anything.
it just lacks the "why should be natural to take the derivative of the inside". pretty important this part what i mean is something like "then, you realize that the first power rule was just the derivative with respect to the inside, not x" great vid, anyway
How do you use the limit definition of derivative (which you used in the first part of the video) to find the derivative of x^(2/3)? I keep getting stuck. Thanks!
The derivative is defined to be the slope of the tangent line. And you get the slope of the tangent line as the limit of the slope of all the secants going through the point (x,(f(x)). And if the second point of the secant has the coordinates (x+h,f(x+h)), you get that its slope is given by ( f(x+h) - f(x) ) / h.
Bah, power rule is for lazy people who have better things to do with their time than derivatives of functions, like running, drinking or watching TH-cam videos (as _ridiculous_ as that sounds!!!). A true mathematician will remain true to their craft, and stay locked indoors at a desk doing all of their derivative calculations from 1st principles.
It's always interesting to see someone working from first principles. Maybe a better explanation of where the 3 come from in your second method for dummies like me; if the function within a function is not considered, then you have not found dy/dx but dy/d(3x+1). To find dy/dx: dy/dx=dy/d(3x+1)*d(3x+1)/dx. One can then legitimately cancel out the d(3x+1)s. Just a thought.
wait so all this time I been sitting on my damm table play with derivative and actually create a chain rule for derivative without even know it even existed. I'm must be Jesus \●_●/
Roman Bykov You can also demonstate it with linear composite functions, try an example with f(x)=ax+b and g(x)=cx+d then find f(g(x)) and examine the slope.
blackpenredpen pliiiiiiz if u re reading this do an explanation of the 6th question in the mathematical Olympiad 1988 cz i don t know if it was interesting pliiiiiizzzzz
I have an idea: prove all the derivative rules using “the definition”
Prove product rule, quotient rule, chain rule etc
didnt dr.payem do the product rule already?
Michael Bobman The chain rule is not at all complicated. In fact, it is far more intuitive to prove with algebra than the product rule.
You can visit KhanAcademy channel for this. He explains them very well.
@@angelmendez-rivera351 it's complicated. The algebra "proof" of multiplying by [g(x+h)-g(x)]/[g(x+h)-g(x)] is mathematically incorrect.
@@SimsHacks It isn't.
My way is to call it 'Function of a function' rule. Because that describes it so much better.
#yay I love how in one video, your topic is pretty advanced, and the next video you deal with something really basic, and you don't start saying "obviously" and talk down to your audience. You treat every topic like it is just as important as any other.
Yay!!! Thank you!!!
I do have a wide-range of audiences with different backgrounds and interests. Hopefully this works : )
Chen-Lu strikes back!
Dani Borrajo Gutiérrez yup!!
YAY!
And the third way....
y = (3x+1)^(1/2)
y^2 = 3x+1
derive
2y*dy/dx = 3
dy/dx = 3/(2y)
dy/dx = 3/(2*(3x+1)^(1/2))
Personally I like the expanded form because then I can see if I missed anything.
it just lacks the "why should be natural to take the derivative of the inside". pretty important this part
what i mean is something like
"then, you realize that the first power rule was just the derivative with respect to the inside, not x"
great vid, anyway
Nice video. I also like 3b1b's video on the chain rule, it really helps to build the intuition of why you multiply by the derivative of the inside.
Dr Peyam says "Use the Chen-Lu" its like martial arts XD
Hi blackpenredpen, can you find this sum s= cos(x)+a*cos(2x)+a^2*cos(3x)+...+a^(n-1)*cos(nx).
[f(x)]^2 = 3x+1
2f.f' = 3 (Derivation)
f'=3/(2f)
Black Chain rule Red Chain rule!
*Black Chen Lu Red Chen Lu
In the next video please explain what is converge and diverge, and how can we know a series is converge or diverge?
Do we always put f(x+h) - f(x)/h to find the derivative? Thanks.
yes
@@blackpenredpen thank you
Great video!
jayson zamora yay
You are my Einstein of calculas
00:04 and 00:24 - What is the name of this font?
that limit problem is hella easier if you do the difference quotient in respect to y. dy/dx=lim k->0 k/(x(y+k)-x(y)). x=(y^2-1)/3
Wow I didn't know you could differentiate that equation with first principle. This was a great video.
If a function can't be differentiated from first principles then it can't be differentiated.
Martin D , I'll keep that in mind
How do you use the limit definition of derivative (which you used in the first part of the video) to find the derivative of x^(2/3)? I keep getting stuck. Thanks!
Mike Schieffer
Use the identity :
a^3-b^3 = (a-b)(a^2+ab+b^2)
Replace a and b with (x+h)^(2/3) and x^(2/3).
Thank you Martial Ribault! #blackpenredpen made a video that uses your suggestion. See it at th-cam.com/video/PDXUg0btWuY/w-d-xo.html
Consider this like a composite of functions f•g ?? f(x)=x^1/2 and g(x)=3x+1
A link to a proof of the chain rule is missing... or will there be a new video?
the more I watch his videos the more I want a gigantic white board on my wall
If you're learning the chain rule you might wanna watch the episode of "essence of calculus - 3b1b" about it. Really intuitive(as always)
Can someone please explain why the defention of the derivative is the definition of the derivative?
The derivative is defined to be the slope of the tangent line. And you get the slope of the tangent line as the limit of the slope of all the secants going through the point (x,(f(x)).
And if the second point of the secant has the coordinates (x+h,f(x+h)), you get that its slope is given by
( f(x+h) - f(x) ) / h.
How can you NOT like the power rule?
Bah, power rule is for lazy people who have better things to do with their time than derivatives of functions, like running, drinking or watching TH-cam videos (as _ridiculous_ as that sounds!!!). A true mathematician will remain true to their craft, and stay locked indoors at a desk doing all of their derivative calculations from 1st principles.
Bah right back, the limit definition is far from first principles. Prove it using a set-theoretic approach to calculus each time, I say!
@@lx4half751 Yeah! I use the definition every question. Not sure why I run out of time after the second question, though.
What is the chain rule ?
Can you explain when to use the chain rule?
How can we generalize the chain rule
If you have got f(g(x)) the derivative = f'(g(x)) • g'(x)
If we have the function y(u) and u is a function of x,
The derivative y' = y'(u)*u'
Djdjcjcjcj Jfnfjfidnf Thanks man. Realises just that two minutes after posting tho ;)
I may do a proof later on.
blackpenredpen, YAAAY!!
Can you evaluate (i^i+1/i^i)^(1/i)?
I love it, it is very useful for kids, keep it up mate, OOO
Hey, I have a question. Can I drive with respect to n a function of x derived n times?
idk
blackpenredpen
what are the best books in mathematics for college student
Young are a brave lecture. Please do applied mathimathics?
Calculus 2
Help!! I want to contact blackpenredpen to send him a tricky integral but I dont know his email
great channel with excellent explanations, Love it!
Thanks for this very helpful video!
My school only taught me how to use the rules but never learnt about the definition of a derivative...
i think you need a new black pen
MatrixWolf yea....
I'm in your video, YAY!!! So satisfying. : ) Thanks, man. Nice CHEN LU.
Snejpu yup!!!! Yay!!!!!
Wonderful video blackpenredpen! I have a question for you, which country do you come from? I come from Hong Kong!
Thanks a lot! This is a very good video!
Gonçalo Freitas my pleasure!!!
Love your videos and think you do a great job.
I love the lim definition
The chain (gang) rule is do what the boss tells you to do. Pretty much like the rules of calculus.
Chen Lu for President! Nobody would be better than the last two lol.
That was nice for me get this refreshed :-)
Black Chen🖋️ Red Chen 🖌️
LUUUUUUUU!!!!!
Love your vids!!!
Yogev Simonovich thanks
anybody recommend any good books on calc
Mike Onega James Stewart has the best books on calc in my opinion
It shows us that we need the chain rull but it does not tell us why other than "if you don't it's a wrong answer".
Great video
11:26 u mean the chen lu? :D:D
Use the chen lu!!
Yo ! I love your video dude, can you integrate (1/a)arctanx(1/x) ? thank you ^_^ the answer is (1/a)(arctanx)(x/a) "normally"
Back in black!
Yup!
Are you graduate student?? If so, what is your area of research?
It's always interesting to see someone working from first principles. Maybe a better explanation of where the 3 come from in your second method for dummies like me; if the function within a function is not considered, then you have not found dy/dx but dy/d(3x+1). To find dy/dx:
dy/dx=dy/d(3x+1)*d(3x+1)/dx. One can then legitimately cancel out the d(3x+1)s.
Just a thought.
pre-calc Mean Value Theorem = calc Chain Rule. NICE
Great video as always! Are you going to do any number theory video soon? #YAY
SpikePowerHD I will try. My mind has been all over the places lately...
blackpenredpen thanks anyway, I don't want to stress you don't worry! :)
Use the Chen Lu!
You got a blue marker!
YaY!... Chen lu..
Skip to the final answer: 7:41.
#Hooray #BPRP 🤘😁🤘
yup
love your videos, wish you were my teacher!!!!
Bernardo Fricks thank you!!! And well, I am, on YT :)
where was this when i was learning it #yay
MiniMawile303 aww. But it's here :)
Real men use the definition of derivative.
Sir are you Japanese or Chinese please sir asking honestly
hi!
Oon Han yay
black pen red pen yay
Sorry for off-topic, may i ask something silly 😂 - do you know chinese? 😂
Marco Yeung Yes, I do.
He's from Taiwan I believe
#yay use the Chen Lu!
Chen-Lu
L-hospital be like : am I a joke to you
😂😂😂
That's not a good way to make students understand , try using composition of functions instead. Btw you're doing a good job .
wait so all this time I been sitting on my damm table play with derivative and actually create a chain rule for derivative without even know it even existed. I'm must be Jesus \●_●/
still not really clear why you have to take the derivative of the inside, if you already took the derivative of the whole thing
Roman Bykov You can also demonstate it with linear composite functions, try an example with f(x)=ax+b and g(x)=cx+d then find f(g(x)) and examine the slope.
Chen lu! #yay
Yay!!!
#yay ft: CHEN LU!
Yeeeeeeh!
Yay!!!!!
blackpenredpen pliiiiiiz if u re reading this do an explanation of the 6th question in the mathematical Olympiad 1988 cz i don t know if it was interesting pliiiiiizzzzz
It's a very hard problem and I am not 100% sure on how to solve it. Sorry.
曹老师～
Kimchi Koalaa hiii
Chen lu
Yes! The most powerful lu ever!!!
11:10 Math Punk jajajajaaj
#YAAAAAAAYYY
= )
Blackpenredpen #yay!!!
Futfan yesssss!!
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Medpop hahaha yea!!!!
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yeaaaahhhhh! #yay
Theodore Jonathan : )
Hi
#yay🙏 thank you
#YAY!
Richard Freeze yes!!
Yaaay
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Obinna Nwakwue yay!!!!
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Crazy Drummer yup!!!
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IQ over 9000
YaY
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#yay
You haven't answered the question about your age!
Αντε γεια ti se endiaferei lol
Coming soon since my bday is coming soon.
first