the derivative with respect to time, the derivative with respect to time, the derivative with respect to time, the derivative with respect to time, the derivative with respect to time, the derivative with respect to time, the derivative with respect to time...

@Odeh

9 ай бұрын

His tutorials are really good but yeah that "derivative with respect to ____" always just makes me a little more confused

@isavenewspapers8890

4 ай бұрын

⁠​⁠@@Odeh"the derivative with respect to _____ " basically just means "the rate of change as _____ changes".

you are sent from heaven. you are a good dude. thank you for these videos. im gonna get my degree probably cause of you. keep up the good work, bro

I think it is important to point out that there is no physical reality to this, and that it is a mere exercise in math. But the exercise is to prepare us for a similar math process that tells us how the area of a sphere changes with time and that DOES have a physical reality. Most math relationships, and there's an infinite number of them have no meaningful physical application (such as the third derivative of position with time), but those few that have application are profoundly important.

I have just understood. thanks

Thank you a LOT Sal..

this was excellent! please have more calculus word problems

Sal is great 3:45 #rules Derivative of constant * something you can take the constant out 4:30 #rules Chain Rule - well explained

@manny4239

4 жыл бұрын

Why are you just able to take a constant out, is it because it derives 0, which makes it disappear, so how is it reasoned that you can just take it out

What a good video!

I love this guy's videos, but sometimes the way he repeats things, repeats things. It gets to be a little distracting, a little distracting.

@EagleEye1104

10 жыл бұрын

true, but actually i hear that repetition subconsciously helps with absorbing the material. it annoyed me a bit but I found myself paying attention a little more.

@perfectdarkzero9

10 жыл бұрын

I could see how that could help a bit, but sometimes I'm just like, "get on with it man!!" lol

@HoshinoMirai

8 жыл бұрын

+Dylan D'Alatri Well I guess you also need to know that his native language is not English. Sometimes it just happens. Same with me.

@Ms452123

6 жыл бұрын

How is his native language not English, i know his parents are from Bangladesh, but he was born and grew up in the U.S, which makes English his native language. Bengali is his parents native language while English is his. There's literally no mistakes in his speech, plus he has a higher mastery of the language than the average American.

@SumaiyahFatimafangirl

5 жыл бұрын

@@HoshinoMirai lmao his native language is english

Yep, Derivatives is used in finding rates, velocity, any changes in times, size,etc.

Great!!

I actually find it really helpful since math is pretty hard for me. If it bothers you, just fast forward :)

I Respect Him for THAT

I paused the video and tried to solve it before him, what I did was; since A is equal to pi r^2 then just take the derivative of pi r^2 with respect to t, using the chain rule: (the derivative of pi r^2 with respect to r) times (the derivative of r with respect to t), and so it will be equal to (2pi r) times (the derivative of r with respect to t, which equals to 1 according to the question) so (2pi rcm) times 1cm/t is just (2pi r cm^2/t) then replacing r with 3 gets us left with 6pi cm^2/t. Isn't this way easier? Or is understanding to do it how he did is important?

U r genius

Raise your right eyebrow every time he says "Rock"...

The rate which the area is growing is different to each value of radius. you forgot to mention that the number you found is the rate that the area grows when the radius is equals to 3 cm. At 6:29 you said that r is 3 cm but you forgot to said that if we want the rate of any other value of radius, we won't use 3, because it would have changed according to the dr/dt.

@Buddy-qb8sw

5 жыл бұрын

I love you

@neo-babylon7872

3 жыл бұрын

Yes thank god that was freaking me out. Thought maybe I missed something.

i feel like my mind is like a machine

The chain rule thing doesn't make any sense to me. I can see where you might use it if you had [r(t)]^2, but then you have the bizarre case of the derivative of a function (what's the derivative of f(x)? Well you have to define the function). Whatever he's getting at here it's not at all as straightforward as he makes it seem.

@ntokozotheo5898

2 жыл бұрын

I also find it confusing

If you are unfamiliar with the derivative, there are a lot of prior videos explaining it.

guys a question on this, shouldn't the rate of how the Area increases not depend on the actual Radius of the circle at a specific time? i mean if you see the answer you can clearly see that the rate for a already formed circle with 3cm on radious at that time is going to have a different rate against a circle with 1cm at that time but with the same increase of cm/sec

@isavenewspapers8890

6 ай бұрын

The rate of change of area does indeed depend on the radius.

Thx it help on my 7th trade finals

@isavenewspapers8890

6 ай бұрын

Calculus in 7th grade?

omg. at first i was like oh yeah i like this guy. he's explaining it so simple. then... like you kept adding things. i knew exactly what to do for my next step but you kept adding "to make sure." There were times you just confused me but thanks for the video anyway. i've watched many related rates video and got it down finally. just gotta be careful.

Isn't it strange that if radius is changing by 1 cm, that means area goes from 9pi to 16pi and the change in area is 7pi. I don't see how derivatives are supposed to explain the change in area in a second?

@isavenewspapers8890

6 ай бұрын

The derivative isn't about finding the average rate of change over a 1-unit interval; we don't need calculus for that. It's about finding the average rate of change over smaller and smaller intervals and taking the limit as the size of the intervals approaches 0.

What are you using in this video to draw?

@jaredmorales9763

4 жыл бұрын

Facts

@prodjvenchy

3 жыл бұрын

@@jaredmorales9763 he isn't using facts

@calebnetsanet1844

3 жыл бұрын

@@prodjvenchy lmfao

So So in in this this case case its its literally literally just just multiply multiply the the Area Area formula formula by by the the rate rate of of growth growth.

@isavenewspapers8890

6 ай бұрын

That's the circumference formula.

@voltrixgames4375

6 ай бұрын

@@isavenewspapers8890 that’s that’s the the circumference circumference formula formula

so many videos are posted that there are no views for an amount of time

ya let me just change that to blue, oh no thats purple, perfect, oh wait thats too dark, whoops

who put you in charge?

I hear him saying derivative, and I am wondering, is this calculus?

@masonbot7440

4 жыл бұрын

PoweredMinecart McUnite yup, np for 6 year response

Well, there is some unclear moment. Okay, 6pi, but let's find area at 3 cm radius = 9pi, at 4 sec = 16 pi, so if we divide A(4sec)/A(3 sec) we get 4/3(not 6 pi), it's a rate of growing area between 3 and 4 sec. So where is here mistake?

@jdlopez131

2 жыл бұрын

actually, I'm equally confused except that I would say that the area changed by A(4) - A(3) which gives me 7pi, not 6

@stickmanbattle997

2 жыл бұрын

@@jdlopez131 yeah you're right

@isavenewspapers8890

6 ай бұрын

That's the wrong way of thinking about it. Your method gives the average rate of change of area over the course of 1 second, but what we want is the rate of change at a single instant. To do this, you can think about finding the average rate of change over smaller and smaller intervals, like 0.1 seconds and 0.001 seconds. The derivative is whatever this rate of change approaches as the size of the interval approaches 0.

Too much emphasis on the derivative with respect to time and not enough emphasis on the chain rule: dA/dt = dA/dr · dr/dt.

I believe he has those already, go to his channel uploads and try looking throught the.... 3,411 videos... right... Oh here you go watch?v=ANyVpMS3HL4 I searched "derivative khan academy"

this is so confusing why calculus gotta be so extra

@prodjvenchy

3 жыл бұрын

nvm i got it but sal you kinda missed on this one. made it way more complex then it needed to be imo. its sad cuz u always have bangers but this one was a miss. i had to watch a vid by an organic chemistry tutor to understand this.

Hehe soup

Why was it necessary to constantly repeat yourself?