So in partial derivatives, when does the constant turn into 0, when does it vanish ans when does it stay untouched?

none of the above

:c

You treat all other variables as constants

Then you just apply the ordinary rules for derivatives

Please explain. Do we just leave the constants as they are?

To take a partial derivative of $f(x,y)$ with respect to $x$ just treat the $y$'s as constants, and take the derivative of $g(x) = f(x,y)$ as you usually do

@NovaliumCompany I'm not sure what you want me to explain. You just treat the other variables like you would treat constants when taking an ordinary derivative

How do we treat constants? Turn them into 1?

So if $f(x,y) = x^2 + y^2$ then taking the derivative of $g(x) = x^2 + 3^2 = f(x,3)$ would be the same as taking the derivative of $g(x) = x^2 + y^2 = f(x,y)$ (where $y$ is a constant in the expression $g(x) = x^2 + y^2$).

As far as I know, derivative of a constant is equal to 0. So we turn all constants into 0?

@NovaliumCompany No, you still have to apply things like the product rule

The derivative of $f(x) = 2x$ is $f'(x) =2$, not $f'(x) = 0$, after all

So constants that are not multiplied are turned into 0, constants that are, are turned into 1?

I don't understand how you think that 2 is "turned into" a 1 there

When you take the derivative of $f(x) = x^2$ what you're doing is forming $f(x + h) = (x+h)^2 = x^2 + 2xh + h^2$ and subtracting it from $f(x) = x^2$ to get $f(x+h)-f(x) = 2xh + h^2$ and then you're dividing it by $h$ to get $\frac{f(x+h)-f(x)}{h} = \frac{(x+h)^2 - x^2}{h} = \frac{2xh+h^2}{h} = 2x + h$, and then you're taking the limit as $h$ goes to zero, $f'(x) = \lim_{h \to 0} \frac{f(x+h)-f(x)}{h} = \lim_{h \to 0} (2x + h) = 2x$. This is how you take derivatives properly.

Ahh.... I'm confused.

This is why the derivative of a constant is zero, because if say $f(x) = 3$ then $f'(x) = \lim_{h \to 0} \frac{f(x+h)-f(x)}{h} = \lim_{h \to 0} \frac{3-3}{h} = \lim_{h \to 0} \frac{0}{h} = \lim_{h \to 0} 0 = 0$.

I'll go to bed, I'll try again tommorow. Thanks guys. (also I'm on phone, not LaTex so @bolbteppa I'll see your stuff tommorow, thanks)

If you don't understand this I wouldn't even be looking at partial derivatives

It will just confuse you even more

I have no LaTex on phone, I probably understand them

There's a reason why calculus books spend about 10 chapters on functions of a single variable before even introducing functions of several variables and their partial derivatives

@NovaliumCompany Protip, avoid multivariable as much as possible until you thoroughly finish a single variable calc book

@SirCumference ok

I'm getting flashbacks to school when going back to the definition of a derivative: Just after we'd learned what it was, we took an exam, and the gal next to me just copied what I wrote. I made a very silly but very particular mistake, and she copied it, so we had to explain how that happened

Multivariable calc is kind of like single variable calc on crack. It's extremely easy to become confused if you don't have a strong single variable background.

Literally not a single boy sits around/next to me in school

If multivariable calc is om crack, maybe me getting on crack would help ::Dd

Of all the times I saved my classmates from failing a class, that was the only time we were caught :P

@ACuriousMind I guess your teacher couldn't differentiate between your tests

Sorry

@SirCumference ba-dum-tss

teacher needs some milk

Why am I still here. I need to sleep.

It's not even midnight

It'd be really awesome to meet one of you in real life :p

@ACuriousMind Bulgaria

Sooo...it's a bit past midnight?

yah

Bulgaria should be an hour off from us at most

12:34

@ACuriousMind was Gal hot :pp

sorry i had to ask, Im still a teenager and most of the time my fingers are having a mind of their own

@NovaliumCompany I resent the implication there.

@ACuriousMind sorry.

@NovaliumCompany I mean that I dislike the idea that that's of any importance

A pretty girl sits next to me

Sorry but f*cking puberty

...

@ACuriousMind How do you imagine me irl?

But, alas, I was a teenager once. It will pass, and you will have a great many embarrassing stories to tell :P

I'm kinda using this chatroom as a therapy to get out some personal thoughts and concerns sometimes /

@ACuriousMind How old are you sorry?

@NovaliumCompany I...don't? One thing I like about the internet that we don't have to have full "pictures" of what we are like

@NovaliumCompany ::counts:: 26

@ACuriousMind Internet communication gets rid of emotions and mostly focuses on cognitive information

Donno if that made sense but

@ACuriousMind I can guess you are a guy who reads a lot, has some (not many) friends, goes out for a beer regularly

> has some (not many) friends

Damn son

@NovaliumCompany It is purely verbal communication as opposed to non-verbal communication, which is not quite the same

@SirCumference Smart people like him are rarity

@NovaliumCompany Yeah but the "not many" is a pretty harsh assumption :P

Sorry :p

@NovaliumCompany I sometimes have to call off things with my friends because it gets too much (I'm very much an introvert who recharges by being on their own), but I never wish I had less, so I'd say I have about the right amount of friends for me

I have 0 friends :cc

I'll fix it in the future when I finally get away from Bulgaria

Finding friends wirlth similar interests is hard here

Everyone is obsessed with wasting their time, and here I am at home reading

Can't help you with that, I was always a big fan of wasting my time :P

@ACuriousMind By wasting time I mean, going out and getting drunk, just hanging around...

@ACuriousMind You don't happen to know if mathjax works on tag wiki excerpts, do you?

Oh hey, you're a mod now @Mithrandir24601?

@Mithrandir24601 I'm pretty sure it doesn't

@ACuriousMind OK. Ah well, thanks

The closest I've got to having friends with my interests is here in this chatroom.

@SirCumference I've got a gold badge from it, so I've been a mod for over a year now :P

Alright. Goodnight guys +)

@NovaliumCompany I'll be honest...I had no friends with my interests until I started college and met people in my major.

@SirCumference Ye, makes sense

Why are there like 3 people who never leave this chatroom?

I'm going to spend a week with my oldest friends at a festival a week from now. None of them really shares any interest with me beyond liking metal. Yet that's fine, and it's always a blast.

@ACuriousMind metal. wow, that I did not expect :D

Ok I need to go to sleep, further messages will not be processed by my consciousness

physics.stackexchange.com/questions/491843/…

@Ten Probably because different physics disciplines prepare people very differently for the job market

@NovaliumCompany you'd be very surprised by what @ACuriousMind 's interests are