chain rule for derivative but why do we need it, calculus 1 tutorial 

I have an idea: prove all the derivative rules using “the definition” Prove product rule, quotient rule, chain rule etc

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.

Chen-Lu strikes back!

Dr Peyam says "Use the Chen-Lu" its like martial arts XD

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.

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

Hi blackpenredpen, can you find this sum s= cos(x)+a*cos(2x)+a^2*cos(3x)+...+a^(n-1)*cos(nx).

Black Chain rule Red Chain rule!

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.

Wow I didn't know you could differentiate that equation with first principle. This was a great video.

In the next video please explain what is converge and diverge, and how can we know a series is converge or diverge?

I'm in your video, YAY!!! So satisfying. : ) Thanks, man. Nice CHEN LU.

[f(x)]^2 = 3x+1 2f.f' = 3 (Derivation) f'=3/(2f)

You are my Einstein of calculas

Great video!

the more I watch his videos the more I want a gigantic white board on my wall

I love it, it is very useful for kids, keep it up mate, OOO

If you're learning the chain rule you might wanna watch the episode of "essence of calculus - 3b1b" about it. Really intuitive(as always)

Do we always put f(x+h) - f(x)/h to find the derivative? Thanks.

great channel with excellent explanations, Love it!

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!

Love your vids!!!

Consider this like a composite of functions f•g ?? f(x)=x^1/2 and g(x)=3x+1

Thanks for this very helpful video!

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

Love your videos and think you do a great job.

Young are a brave lecture. Please do applied mathimathics?

How can you NOT like the power rule?

Thanks a lot! This is a very good video!

Can someone please explain why the defention of the derivative is the definition of the derivative?

Chen Lu for President! Nobody would be better than the last two lol.

i think you need a new black pen

That was nice for me get this refreshed :-)

Hey, I have a question. Can I drive with respect to n a function of x derived n times?

Great video

Wonderful video blackpenredpen! I have a question for you, which country do you come from? I come from Hong Kong!

I love the lim definition

love your videos, wish you were my teacher!!!!

blackpenredpen what are the best books in mathematics for college student

My school only taught me how to use the rules but never learnt about the definition of a derivative...

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"

YaY!... Chen lu..

The chain (gang) rule is do what the boss tells you to do. Pretty much like the rules of calculus.

Can you explain when to use the chain rule?

hi!

Sorry for off-topic, may i ask something silly 😂 - do you know chinese? 😂

Can you evaluate (i^i+1/i^i)^(1/i)?

Great video as always! Are you going to do any number theory video soon? #YAY

Help!! I want to contact blackpenredpen to send him a tricky integral but I dont know his email

#yay use the Chen Lu!

Use the Chen Lu!

A link to a proof of the chain rule is missing... or will there be a new video?

Back in black!

00:04 and 00:24 - What is the name of this font?

pre-calc Mean Value Theorem = calc Chain Rule. NICE

anybody recommend any good books on calc

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where was this when i was learning it #yay

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.

Use the chen lu!!

How can we generalize the chain rule

What is the chain rule ?

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black pen red pen yay

You got a blue marker!

Chen-Lu

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".

Blackpenredpen #yay!!!

11:26 u mean the chen lu? :D:D

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#yay🙏 thank you

Are you graduate student?? If so, what is your area of research?

YAY!

11:10 Math Punk jajajajaaj

#yay !

Sir are you Japanese or Chinese please sir asking honestly

L-hospital be like : am I a joke to you 😂😂😂

#yay

曹老师～

Real men use the definition of derivative.

#YAY!

Yay

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 \●_●/

That's not a good way to make students understand , try using composition of functions instead. Btw you're doing a good job .

Yaaay

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Chen lu

Hi

still not really clear why you have to take the derivative of the inside, if you already took the derivative of the whole thing

YaY

IQ over 9000

Skip to the final answer: 7:41. #Hooray #BPRP 🤘😁🤘

#yay You haven't answered the question about your age!

first

love you man, please pin my comment it would make my day