what the FUCK is the difference between these three?
I know that two/three is used for partial derivatives as opposed to one... but I have seen them used interchangeably in the same context.
I have ALSO seen them used for separate values in the same context.
Prof gave me a funny look when I asked, so i'm taking my autism to you Veeky Forums
Isn't it obvious?
show me 1 (one) example of III
...
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.
The funny thing is that none of those are Daucus carota.
I is a differential form, while III is codifferentiation.
(sick roll btw)
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'?
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.
Thanks a lot mate
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
"small change" is nonsense mathematically speaking.
I draw my x like op too... let me see yours
no it isnt
This is why you die. Also, some are Daucus carota.
>differential, partial derivative, variation
brainlet alert
In general, from left to right:
>Total derivative, or differential
>Partial derivative, or surface
>Variation in [math] x [/math], or "an infinitesimal increment"
You obviously have no idea what calculus of variations is, right?
Anyone saying anything other than is automatically a retard
Yes it is, unless you're doing nonstandard analysis and you'd call it infinitesimals, but I'm guessing you're not.
mathematicians don't use delta for variation, not so much. That's a physicist thing.
Came here to post this
Feels good being an engineer
Shut the fuck up, engicuck. You're even more brainlet tier than he is
You're right.
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.
What was that? Sorry, couldn't hear you over all the money I'm making while shitposting on Veeky Forums
(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).