/sci/ - Science & Math

[Anonymous No.10756931]

This is literally the most accurate, simple, and perfect way to describe, define, and explain derivatives. Prove me wrong. Protip: You literally cannot.
Pic related, my OC

[Anonymous No.10756935]

>>10756931
Define "simple"

[Anonymous No.10756937]

>>10756935
Including all relevant necessary facts in concise form, while not including any unnecessary facts

[Anonymous No.10756939]

>>10756931
you’re so dumb jesus christ

[Anonymous No.10756947]

>>10756939
How so?

[Anonymous No.10756948]

I don’t get the significance of this explanation over literally any other

[Anonymous No.10756953]

>>10756947
see >>10756948 you massive brainlet

[Anonymous No.10756956]

>>10756948
Ok so then you can't name a single advantage of any other definition or explanation?

[Anonymous No.10756958]

>>10756953
see >>10756956 you massive brainlet

[Anonymous No.10756964]

>>10756931
Well, you've failed to define f, x, y, delta, dx, or dy. That's pretty fucked imo.

[Anonymous No.10756968]

>>10756964
I implicitly defined dy and dx by saying that dy/dx is delta y/delta x as delta x approaches 0 (that is, dy=delta y as delta x approaches 0, and dx=delta x as delta x approaches 0). I don't think that needs to be explained.

You are correct that I did not define f, x, y, or delta. But f, x, and y are obvious to someone even before beginning to learn calculus as function, input variable, and output variable. So the only point you even kinda maybe have is that I didn't define delta, but it is implicit that when explaining deravitves to someone, they will be told that delta means change in

[Anonymous No.10756972]

>>10756931
central difference be more accurate, yo

[Anonymous No.10756973]

>>10756931
ok

[Anonymous No.10756982]

>>10756931
it's almost as if that's literally the fucking definition

[Anonymous No.10756985]

>>10756931
I'd do something more verbal, like:
Derivative is slope (rise over run).
For an arbitrarily small run (distance) between two points.
Because you want it to be slope at a point with 0 run.
But you can't use actual 0 as your run because that would mean dividing by 0.
So you move towards (but not fully to) 0 instead and see what the slope is approaching.
You can plug in different functions to that rise over run scheme where instead of 0 you're using almost 0.
Doing this is convenient because you can treat almost 0 like actual 0 and let it drop out of your equations.
Since this way of getting slope at a point can be used to find slope along many different points of a function, what you've really done is come up with a new function.
This is done in real life all the time, like with the concept of acceleration which is the derivative function of velocity relative to time i.e. how much velocity is increasing as time increases.

[Anonymous No.10756987]

>>10756968
>I implicitly defined
>I don't think that needs to be explained
>But f, x, and y are obvious to someone even before beginning to learn calculus

You have an intuitive grasp on the relevant concepts. That might be suitable for explaining to someone else who only needs an intuitive grasp themselves. Your definitions are pretty atrocious for anyone trying to rigorously prove anything about derivatives, though.

[Anonymous No.10756988]

>>10756968
>implicitly defined

[Anonymous No.10756990]

>>10756972
What?

[Anonymous No.10756998]

>>10756988
>>10756987
OKAY FINE

[Anonymous No.10757002]

>>10756985
This is good, but if you take
>you can treat almost 0 like actual 0 and let it drop out of your equations.
and run with it, you can probably 'prove' all kinds of untrue stuff
You're right of course, but that concept cannot be applied in all situations.
>>10756987
>Your definitions are pretty atrocious for anyone trying to rigorously prove anything about derivatives, though.
Okay then what is the best way to rigorously prove something about derivatives?

[Anonymous No.10757003]

>>10756998
So dx and dy are 0?

[Anonymous No.10757005]

>>10757003
No, they are infinitesimal nonzeroes. Kind of like .999... is not actually equal to 1 even though dumbfuck pseudointellectuals claim that it is.
https://en.wikipedia.org/wiki/Hyperreal_number

[Anonymous No.10757007]

>>10757005
Ok, so you are retarded.

[Anonymous No.10757014]

>>10756931
Well there are some simpler ways to define derivatives, for instance, smooth infinitesimal analysis

[Anonymous No.10757016]

>>10757002
>This is good, but if you take
>you can treat almost 0 like actual 0 and let it drop out of your equations.
>and run with it, you can probably 'prove' all kinds of untrue stuff
>You're right of course, but that concept cannot be applied in all situations.
Yeah, you would need to fine tune the idea with whoever you're teaching it too so they know what is and isn't allowed. Mainly would be stuff they already know about though like don't divide by 0.
That's where the argument for rigorous definitions starts to take over I guess.

[Anonymous No.10757031]

>>10756931
>This is literally the most accurate, simple, and perfect way to describe, define, and explain derivatives.
No. It's a way to make a note of it. And you have infinitesimal non-numbers being equated to real numbers. Put it in the trash.