Math

[Josh No.5671862]

What is derivative?

[Anonymous No.5671866]

Pop music

[Anonymous No.5671867]

>>5671862
>troll

[Anonymous No.5671881]

>>5671867
How?

[Anonymous No.5671896]

In calculus, a branch of mathematics, the derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's instantaneous velocity.
The derivative of a function at a chosen input value describes the best linear approximation of the function near that input value. Informally, the derivative is the ratio of the infinitesimal change of the output over the infinitesimal change of the input producing that change of output. For a real-valued function of a single real variable, the derivative at a point equals the slope of the tangent line to the graph of the function at that point. In higher dimensions, the derivative of a function at a point is a linear transformation called the linearization.[1] A closely related notion is the differential of a function.
The process of finding a derivative is called differentiation. The reverse process is called antidifferentiation. The fundamental theorem of calculus states that antidifferentiation is the same as integration. Differentiation and integration constitute the two fundamental operations in single-variable calculus.

[Anonymous No.5671956]

>>5671896
>The fundamental theorem of calculus states that antidifferentiation is the same as integration
No it doesn't. It's just common notation to write an integral sign without limits to refer to antidifferentiation.

[Anonymous No.5671984]

>>5671896
tldr;
>derivative=slope

[Anonymous No.5672028]

[Anonymous No.5672070]

The derivative of a real-valued function f in a domain D is the Lagrangian section of the cotangent bundle T*(D) that gives the connection form for the unique flat connection on the trivial R-bundle DxR for which the graph of f is parallel.

[Anonymous No.5672089]

>>5671862
Something derived from something

[Anonymous No.5672093]

>>5672070
lel

[Anonymous No.5672202]

It's a function widely used in differential calculus. It's the slope of a tangent line.

If you imagine a parabola, the derivative is the slope at any given point on the parabola.

[Anonymous No.5673103]

What kind of derivative? Gateaux derivative? Radon-Nikodym derivative? Please be more specific, OP.

[Anonymous No.5674179]

Covariant derivative? Exterior derivative?

[Anonymous No.5674183]

>>5674179
>double panda two-a-days

[Anonymous No.5675459]

Lie derivative?

[Anonymous No.5676851]

Frechet derivative? Nah, too trivial.

[Anonymous No.5677964]

In the discrete case you can work with finite differences.

[Anonymous No.5678032]

>>5674179
If he's asking what a derivative is why the FUCK would he know the difference between the two?

[Anonymous No.5678137]

>>5671862
The doom of the world economy

[Anonymous No.5678178]

>>5671862
my pic

[Anonymous No.5678187]

/sci/ is the only board where self-moderation is impossible

[Anonymous No.5678210]

The derivative

[Anonymous No.5679278]

>>5678032
His question is too vague. We're trying to figure out what kind of derivative he's talking about.

[Anonymous No.5679290]

You take a function of x and you call it y
Take any x nought that you care to try
Make a change and call it delta x
The corresponding change in y is what you find next
Now you take the quotient and now carefully
Send delta x to zero and I think you'll see,
That what the limit gives us if our work all checks
It's what we call dy/dx, it's just dy/dx!

(jazz hands)

[Anonymous No.5679293]

>>5671862
What's with all these fucking Koalas on /sci/ today?

[Anonymous No.5679338]

>>5671862
>Imitative of the work of another person, and usually disapproved of for that reason.
Metal Gear Rising: Revengence because it wasn't made by kojima.
Luigi's Mansion: Dark Moon because it wasn't developed by Nintendo.

[Anonymous No.5679342]

>>5678210

what the fuck is this?

[Anonymous No.5679440]

>>5671862

some operators operate on numbers like plus and multiply.
some operators operate on functions like derivative and integral.

a derivative is asking about the rate of change.
and integral tells you about the area under a function, like how much work and engine does, or how much water flows through a pip.

[Anonymous No.5680686]

>>5679440
>and integral tells you about the area under a function

Integrals can do much more than that.

[Anonymous No.5680984]

>>5680686
im just explaining like theyre 5

[diversity coordinator !D3ux1y2oJM No.5681042]

the function for the instantaneous slope of another function

[Anonymous No.5681082]

>>5672028
>b
>not ∆x

[Anonymous No.5681088]

Instantaneous rate of change. Do you even lift?

[Anonymous No.5681092]

>>5671984
More like tangent of the slope you cocksucker.

[Anonymous No.5681093]

>>5681092
It's actually the slope of the line tangent at that point...

Apparently, now you are the homosexual.

[Anonymous No.5681483]

>>5680984
Why do you do this? We still haven't figured out what kind of derivative OP is talking about.

[Anonymous No.5682796]

>>5680984
>im just explaining like theyre 5

No, you're spouting wrong garbage. >>5672070 explained it like they're 5.

[Anonymous No.5682861]

>>5678210
I fucking fainted because of this gif, fuck you anon, fucking reported

[Anonymous No.5682924]

Change in something with respect to something else.

[Anonymous No.5682939]

>>5679290
>(jazz hands)

i'm going to have to ask you to leave

[Anonymous No.5682964]

f(x)=2x
f'(x)=2

You now have a phd in calculus.

[Anonymous No.5683764]

>>5679293
Where? I do not see any.

[Anonymous No.5684239]

>>5671881
Who are you quoting?

[Anonymous No.5685173]

>>5682964
doesn't work for x = 0

[Anonymous No.5686244]

>>5682924
That's very vague. Can you be more specific?

[Anonymous No.5686265]

>>5685173
Yes, it does. f(x) = 2x. That's a line with slope 2. That's why f'(x) = 2. The line with slope 2 passes through the point (0, 0). The slope of the line at that point is still 2. Therefore, f'(0) = 2.

[Anonymous No.5686268]

>>5679440
what is area?
what is under?

[Anonymous No.5686269]

>>5685173
Yes, it does. f(x) = 2x is a line with slope 2. That's why f'(x) = 2. The line passes through the point (0, 0). At that point, the slope of the line is still 2. So f'(0) = 2.

[Anonymous No.5687647]

>>5686268
lrn2 measure theory

[Anonymous No.5687691]

>What is derivative?

financial instruments
virtual economy
a.k.a. organized crime

[Anonymous No.5688852]

>>5687691
Interesting. Do you have any good sources?

[Anonymous No.5689544]

>>5687691
>>5688852
pls respond

[Anonymous No.5690838]

A chemical compound derived from another compound.

[Anonymous No.5691823]

The result of applying a derivation.

[Anonymous No.5691919]

>>5688852
devilfinder.com/find.php?q=derivative+finance

[Anonymous No.5693241]

>>5691919
WTF is that site? Looks like a google without the google logo.

[Anonymous No.5693284]

>>5671862
>>doesn't know what a derivative is

[Anonymous No.5694536]

>>5693284
This is a non-trivial question. I'm sure you don't know ALL meanings of derivative.

[Anonymous No.5695051]

>>5678210
fuuuck that hurts my eyes

[Anonymous No.5695405]

>>5671862
voices

[Anonymous No.5695840]

We just don't know.

[Anonymous No.5696648]

Seriously, what is it?

[Anonymous No.5697592]

Why?

[Anonymous No.5698584]

derivative bump

[Anonymous No.5699482]

[Anonymous No.5699876]

http://en.wikipedia.org/wiki/Derivative