Captcha

fuck gimp

I bet my boy Wolfram (the alpha) Alpha knows

6

>Single variable
>Partial derivative

how else would you write it? dy/dx?

how else do you want to write it, faggot? it's the usual notation

I don't know, maybe d/dx?

that's exactly what it says you tremendous retard
\partial is how you write that d

>fucked by the GiMP
found the no-talent MS Paint user

>[math]\frac{\partial }{\partial x}[/math] and [math]\frac{\mathrm{d} }{\mathrm{d} x}[/math] are the same in this retard's eyes
How was that calc I final?

>3
its trying to find out if i'm human, only goblins, trolls, and AI can solve that equation; therefore giving the wrong answer will get me through.
Stay mad you brainlets :^)

I'm a grad student
ask me how I know you're just taking calculus

Lowercase delta is pretty much d. Who cares?

I don't give a shit if you're a fag student. You're the one defending using partial derivatives for single variable functions

And then there's this faggot

>You're the one defending using partial derivatives for single variable functions
yeah... that's what people do....
I personally use D mostly but who cares

the truth is no one cares. as much as your teacher must have said to you "okay now in multivariable calculus, the notation is different!!!!", it's the same shit

No it isn't

No it isn't

What's the difference?

only a retard would argue about something as meaningless as this
ask the faculty in the math department, make a poll. who cares? do you care? they don't

Multi versus single variables

Maybe not at your brainlet shit-tier degree mill, but at my uni (top 20 in the world), you'd get points off if you wrote a fucking partial derivative symbol for f(x)

>you'd get points off
in your fake math for idiots class? or in analysis? no one would take points for that in analysis

in fact, I'm not buying it at all. no one would take points off for that in calculus either

he's fucking trolling, d/dx and partials are the same fucking notation when you take a look at context. dumb fuck, stay in school

They should.
Why have different notations when theyre "lmao duh saem"?

I'm actually not

>They should.
they don't. no one cares.
people write it as d/dx because they're lazy
but then idiots go
>hurr let's multiply by the differential xD
so you have to make it explicit that it won't work by putting another symbol

is there a reason for the convention?

Wow I'm stupid I never realized there was a difference between the differential and the derivative

wait can't you (somewhat) easily write a script that solves this captcha?

>Why have different notations when theyre "lmao duh saem"?
Different notation has different meaning when you have more than one variable. Here you have only one, x.

Also sprach Engineer

Anyone who can't write a script to solve this captcha is a brainlet
>what are computers
>literal calculators

What site is this for desu?

>Different notation has different meaning when you have more than one variable
do explain user, go ahead

>Lowercase delta
you mean δ?

Yes, you have one variable, so you shouldn't be using PDs.

And yet there are people arguing against this

no one gives a fuck, both notations are interchangeable, /partial just looks better

If I was a professor I would unironically fail you.

>both notations are interchangeable
>the total derivative and the partial derivative are the same

Where is the second variable?

Unless I'm mistaken that looks like a partial derivative but I only see one variable

only one of us grades calculus exams. guess who?

>"total" derivative
>when you argue online about things you're learning and are convinced the terminology you use is universal
ask me how I know you've never taken analysis

It's literally calc 101 user. df/dx is the total derivative whereas δf/δx is the partial derivative. In the case that f is a function of x only then as per the differential:
df = δf/δx * dx and therefore df/dx = δf/δx.

It is in the case where f is a function of more than x (for instance of x and y) that the total and the partial derivatives do not coincide, as in that case the differential becomes:
df = δf/δx * dx + δf/δy * dy
and therefore
df/dx = δf/δx + δf/δy * dy/dx = δf/δx + δf/δy * y'(x)

Intuitively this is easy to understand. If y depends on x then the "total variation of f with respect to x" (the total derivative) will also incorporate some variation with respect to y since y will vary too. If y'(x) = 0 (if y and x are totally independent) then you get once again df/dx = δf/δx

People who think ∂ is the same as lowercase delta should actually be shot at point blank range

>/delta instead of /partial
>"differentials"
>phrases things in terms of "variation with respect to ..."

the derivative of the function f is the linear function Df such that lim |f(x) - Df(x)| / |x| is zero
ignoring all that for a second, you have not explained how both notations are different. maybe you believe "differentials" make sense, and df/dx is a "quotient of differentials"?

(excuse my super butchered definition, you know what I mean)

I was too lazy to lookup the symbol and just copypasted the delta a few posts above. Deal with it faggot.

>the derivative of the function f is the linear function Df
wat

>ignoring all that for a second, you have not explained how both notations are different.
Spotted the brainlet who doesn't know what a differential is.

>I was too lazy to lookup the symbol and just copypasted the delta a few posts above
[math]\partial[/math], brainlet

>Spotted the brainlet who doesn't know what a differential is.
kek, talk about irony
you're the one that doesn't know the differential is a linear map between tangent spaces
en.wikipedia.org/wiki/Pushforward_(differential)

"differentials" don't exist, you have been tricked in a watered down "math for idiots" course (I'm not going to give you the benefit of doubt and assume you mean differential forms, you clearly have no clue what those are either)
the derivative is indeed a linear function. since you've now made clear that no one has ever told you what the definition is, let me be more careful.

Let [math]f : U \subset \mathbb{R}^n \to \mathbb{R}^m[/math] be a function. The derivative of the function at a point [math]x \in U[/math] is, if it exists, the unique linear function [math]Df[/math] such that

[eqn]\lim_{a \to x} \frac{|f(a) - f(x) - Df(a-x)|}{|a-x|} = 0 [/eqn]

uh, we denote it [math]Df(x)[\math] clearly, not [math]Df [\math]

and here i was thinking we don't need this captcha because most of the board will solve them too easily

>"differentials" don't exist,
Ok bud.

>implying that the whole of something is not also a part of it
gas yourself and then return to /pol/ from whence you came.

imagine being this buttblasted
don't talk about math ever again if you want to avoid the embarrassment

The only one being buttblasted is you.

you're the one who's being all authoritative about your shit when you don't even know what a derivative is buddy

>cornered, no argument left
>oh better throw in a /pol/ boogeyman out of nowhere, that'll get him off my back!
typical brainlet tactics

googled some calc 1 for you faggot
tutorial.math.lamar.edu/Classes/CalcI/Differentials.aspx

not sure how you can say it "doesn't exist" when it's just another formulation of the same concept

>everyone but me is the same person
seriously, back to /pol/

There are obviously multiple definitions of a derivative appropriate for different levels of mathematical understanding. Your autistic clinging to that one definition, which does not help at all in the explanation of the difference between a partial and a total derivative (which was what I was answering initially), shows that you're trying to hide and compensate for a lack of intuitive mathematical understanding with nitpickings about formalism. Sad!

>explain to a brainlet that it doesn't work like that
>he gives me some shitty calc 1 lectures

I'll say it slowly for you. Calculus is watered down math, and teachers are prone to use informal shorthand with no meaning in order to make it simpler for the brainlets.

A "differential" doesn't exist. I'd ask you to define it if you could, but you probably don't know what a mathematical definition is either.

what's your definition of the derivative then? "a ratio of differentials"? those don't exist, brainlet. hence why the notations d/dx and \partial/\partial x are interchangeable and no one gives a fuck

>implying I'm
wew, talk about irony indeed
>>everyone but me is the same person

>the notations d/dx and \partial/\partial x are interchangeable

lim f(x + h) - f(x) / h as h -> 0.

>"a ratio of differentials"?
df and dx are not differentials but infinitesimals you moronic brainlet.

Derivative of a constant is zero.
If x=pi
D/Dx(6*1+3*0)
=0
These chucklefucks will argue about anything.
This is like week two calc. Consider retaking trig.

>implying that I ever implied that you were him
making up shit the other guy didn't say is called "strawmanning", so i'm going to have to ask you to gas yourself.

notice you didn't even address the meat of my argument which was that taking a "part" of something doesn't necessarily imply that something has to be left over.
hence you can take the partial of a 1 variable function, the "part" just happens to be equal to the "whole" in this case.
you obviously couldn't combat this deft and simple defintiion that cuts your legs off, so instead you latched onto the part where I called you a /pol/tard (which, of course, was true anyways)

>lim f(x + h) - f(x) / h as h -> 0.
do you realize it's the same one I posted? or are you too much of an idiot to realize that R is naturally isomorphic to L(R,R) and this takes the definitions onto each other?

>infinitesimals
fucking kek
go ahead and define that one

Why would you go and do that for?

>I called you a /pol/tard
>again implying I'm
you're never going to make it lad

>gas yourself
Back to pol you go too, stormtard.

>do you realize it's the same one I posted? or are you too much of an idiot to realize that R is naturally isomorphic to L(R,R) and this takes the definitions onto each other?
Again with the clinging to abstract formalism over the actual underlying mathematics.

>go ahead and define that one
>he doesn't intuitively understand the concept of an infinitesimal
Like I said, it's sad that you're unable to understand the basic mathematical concepts. An overeducated moron is what you are.

>notice you didn't even address the meat of my argument which was that taking a "part" of something doesn't necessarily imply that something has to be left over.
>hence you can take the partial of a 1 variable function, the "part" just happens to be equal to the "whole" in this case.
>you obviously couldn't combat this deft and simple definition that cuts your legs off
Any objections?

I got a A my teacher was like gud jub.

You a straight goon, nigga. Partial is df/dx ya dangus.

>elementary linear algebra is abstract formalism
lol
>"df and dx are not differentials but infinitesimals you moronic brainlet."
>well, define that
>"An overeducated moron is what you are."
thanks for showing me lad
good luck in your dicksucking career

I just addressed the "part" of your post that was meaningful for my argument :^)
>not knowing the part is only distinguished within the whole in the presence of other parts, and similarly partial derivative only makes sense in the presence of other partial derivatives to distinguish itself from
n e v e r g o n n a m a k e i t

fuck off back to

>t. never heard of calculus of variations

>not knowing the part is only distinguished within the whole in the presence of other parts
reaching hard as fuck now.

good luck with your never going to make a single meaningful contribution to mathematics because I'm too stupid and cloak my insecurities in an autistic obsession with formalism career.

yeah I wish I could discover what differentials and infinitesimals are haha
hmu when you figure out what the derivative is, and let's try

meaning is use, brainlet
not my fault you can't comprehend that

>descending into meaningless platitudes to cloak your confusion
gg.

some words for you to think about as you lick your wounds.
terrytao.wordpress.com/career-advice/there’s-more-to-mathematics-than-rigour-and-proofs/

You obviously have mo idea what you are actually doing when you take the derivative of a function, bro!
It's, like, the limit as h approaches zero of ((f(x+h)-f(x))/h), bro!
Getchoo a tuition refund, nigga: your school is garbage, son.

X=pi, simplify inside the trig functions.

Derivative of sinx is cos, cosx is -sinx. 6cos(1/2pi)=0, -3sin(3/2pi)= -3*-1=3 0+3=3. Have you even taken calc I?

The math works even if you replace ∂ with a farting goat.
You are nothing but a artsy fartsy faggot.
Run along now, there are curtain colors to select or operas to sigh to, or whatever it is you faggots do all day.

>being this mad
It's okay user, belittle other anons in other threads by posting complicated formulas you found on wikipedia to feel smart and better about yourself.

>complicated formulas
lol

Partial derivative is portion of derivative of a multivariable function with respect to one of those derivatives.

In this case, that is implied.

Chuckled

Lolololol