>the derivative of x^2 is 2x
says who? everything that I studied in maths before this point made sense, if you add 2 apples to 3 apples you get 5 apples makes sense, but suddenly they give you derivation rules and tell you to memorize them when they make no fricking sense. they say that's how differentials vary, but if differentials are so small aren't they always about 0?
this point is when maths stops being about useful stuff to calculate things in real life and turns into esotheric madeup nonsense that isn't useful at all
Anything past Algebra 2 is of niche value, at best.
manifold bros just keep winning
>getting filtered by calc 1
Sad
>maths stops being about useful stuff to calculate things in real life and turns into esotheric madeup nonsense that isn't useful at all
it should be legal to turn off someone's water for posts like this.
Lost.
Why is his mom a fridge?
She just is a fridge
>says who?
The definition of the derivative.
who defined it this way? was he stupid?
Have you not learned the first principle way using limits? Just expand x^2 around h. Then derivative is just the ratio of that expansion to h for the limit h -> 0. If you look at it geometrically, that ratio is essentially the slope (rise/run) of tangent to the curve x^2 at x=h. So derivative is just that, slope of tangent of a curve.
Bad news is you already got filtered by this trivial shit.
It's kinda surprising how schools manage to make math as anything but esoteric.
Euler's trigonometry formula is literally voodoo magic yet it had concrete world applications.
[math]
f(x)=x^2 \
displaystyle
lim_{h to 0} dfrac{f(x+h)-f(x)}{h}
= lim_{h to 0} dfrac{(x+h)^2 -x^2}{h} \
displaystyle
= lim_{h to 0} dfrac{x^2+2 xh+h^2 -x^2}{h}
= lim_{h to 0} ~ 2x+h = 2x
[/math]
look i know im an idiot, i dont care. im in calc 1 rn, and i dont get how f(x+h) = (x+h)^2. does f count as x or something? i know, sorry im an idiot. please be slow with me.
If f(x) = x^2 then f(x+h) = (x+h)^2 because the function squares the input and the input here is x+h. Filtered by functions man, couldn't be me.
>old enough to post on IQfy
>struggling with basic calculus
NA education kek. In europe one does real analysis and proof-based linear algebra at age 17. Literally had my bachelors degree at age 21
>h->0
stopped reading there
On the chance that this isn't a bait post, it sounds as if you may be in some, like, "math for economics," "math for the social sciences" class or whatever that just rattles off calculus factoids without worrying too much about fundamental understanding.
[math]frac{d}{dx}x^2 = lim_{hrightarrow 0}frac{(x+h)^2 - x^2}{h} = lim_{hrightarrow 0}frac{x^2 + 2xh + h^2 - x^2}{h} = lim_{hrightarrow 0}frac{2xh + h^2}{h} = lim_{hrightarrow 0}2x +h = 2x[/math]
Thread Closed
>You're supposed to memorize
No Black person you are supposed to understand the semantic content not regurgitate the symbols you saw on the screen
>Math isn't useful
You don't know math so you can't tell. But your intelligence is such that if you did, it still wouldn't be useful.
Practically all of AI today is built on taking derivatives of stuff.
Derivitive is rate of growth. It's saying for something that follows an exponential curve like bacteria multiplying that the rate of growth is twice the time elapsed.
>they give you derivation rules and tell you to memorize them when they make no fricking sense
Get better teachers or a better book. Memorizing derivation rules without understanding them is worse than useless.
Now, integrals are a different beast. That's what filtered me out of math.
son of a fridge