d-d-d-dumbass

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>>9166645
Isn't it obvious?

show me 1 (one) example of III

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>>9166658

>>9166665
this looks like that time OP thought 11 was a weird symbol

[math]x+\delta x[/math] just means x plus a small change in x. It's like the epsilon-delta definition of a limit.

Delta x (III) means 'change in x', this is not a differential at all.

>>9166649
The funny thing is that none of those are Daucus carota.

I is a differential form, while III is codifferentiation.

>>9166666 (sick roll btw)
>>9166686
So just to be clear, III is always meant to represent a small change in x?
Is it bad form to use it like I would 'd'?

>>9166731
Yes, III will pretty much always mean a small change in x.

And yes it's shit form to use it like d or \partial. Readers, and more importantly, your professor won't know what the fuck you're doing if you write \delta.

>>9166733
Thanks a lot mate

>>9166645
dx is for single variable calculus
partial of x is for multi variable calculus
the last one is for quantifying a small change in x
also, your x sucks, it is indistinguishable from a chi

>>9166733
"small change" is nonsense mathematically speaking.

>>9167469
I draw my x like op too... let me see yours

>>9167473
no it isnt

>>9166708
This is why you die. Also, some are Daucus carota.

>>9166645
>differential, partial derivative, variation

brainlet alert

>>9166645
In general, from left to right:
>Total derivative, or differential
>Partial derivative, or surface
>Variation in [math] x [/math], or "an infinitesimal increment"

>>9166666
>>9166731

You obviously have no idea what calculus of variations is, right?

Anyone saying anything other than >>9167489
is automatically a retard

>>9167485
Yes it is, unless you're doing nonstandard analysis and you'd call it infinitesimals, but I'm guessing you're not.

>>9167493

mathematicians don't use delta for variation, not so much. That's a physicist thing.

>>9167489
Came here to post this
Feels good being an engineer

>>9167517
Shut the fuck up, engicuck. You're even more brainlet tier than he is

>>9167515
You're right.

>>9166645
I'm not aware of I being used for anything unless you meant to write d, then it's just the differential. II is partial derivative and to me III is the codifferential.

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>>9167521
What was that? Sorry, couldn't hear you over all the money I'm making while shitposting on /sci/

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>>9166645
(apologies if any explanations are not rigorous, do not use good examples, or vauge.)

The first one (dx, derivative with respect to x if written d/dx) is usually applied to finding the rate of change of a variable of a function. What separates this from the second one is that this term is applied to function of the form y=f(x) wheras there are only two variables, y and x. The term is pretty much used throughout calc 1&2 as well as differential equations.

The Second one is a term used in denotting a partial derivative (in this case, it is a partial derivative with respect to x). What separates the partial derivative symbol from the regular derivative is that instead of looking at the rate of change of an entire function (which is possible to find in two-variable functions like y=f(x) but not functions like z=f(x,y)), it looks at a MULTIvariable function and analyses the rate of change of that function with respect to ONE variable (or one axis if you want to think about it that way). as the multi in multivariable would imply, this term is first taught in multivariable calucus.

The third term? I've only ever seen it used to denote a small change in x (such as a variation like x+deltax). An example where you see a something in the form of deltax is when you first learn the definition of a derivative (although in that case you usually learn it in the form of x+h, where h is some small change in the value of x).