differentiating

[boreal umbra]

does anyone have the patience to teach me the basis of calculus: differentiating? Like, my maths teacher doesnt say shit so i have no clue what anything is. Like what even is differentiating and why is there chain, product and rules for it??? sigh

[small horizon]

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[wintry gale]

First learn first princples, that $\dv{x}[f(x)]=f’(x)=\lim_{h\to 0}\frac{f(x+h)-f(x)}h$, then derive the product and chain rules from it

[uneven mirage]

Kocher

[boreal umbra]

OH yes i rmember that

but i just dont get whats the point of differentiation like what does it even do

[wintry gale]

The reason why they exist is that there is no clean way to differentiate functions like x^3sin(x) without product rule, for example

[boreal umbra]

like i know it somehting slope of line but idk like 🥀

[wintry gale]

It finds the instantaenous rate of change at a specific point of a function

Do you know basic physics?

[boreal umbra]

ummmmmmmmmmmmmmmmmmmmmmmmmmm 🥀

lets be safe and say no

[boreal umbra]

!??!?!??!

😔

[wintry gale]

A tangent line to a curve at that point

[boreal umbra]

but why 😔 liek rjew

[wintry gale]

Consider a car

It tells you the speed in the moment, right?

[boreal umbra]

um

yes

🔥

[wintry gale]

That can be used through calculus

[boreal umbra]

yes..

[wintry gale]

It measures the distance you’ve traveled in a very small time period, and finds the “slope” between those 2 points to get the speed

Derivatives are like a more precise version of that

[boreal umbra]

coz lowkey ive just beenthinking of it as a gradient .. 🥀

[wintry gale]

It is

[boreal umbra]

wait it is

[wintry gale]

,w plot x^2 and 4x-4 on [1, 5]

Damn it

[uneven mirage]

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Requested by exiled_hype

[boreal umbra]

oh gya

i see

[wintry gale]

See this?

[boreal umbra]

yes

[wintry gale]

Do you get it now?

That’s why it’s called a tangent line

[boreal umbra]

OH

OH

OH RIGHT

[wintry gale]

It passes through one point in that local region on the curve

[boreal umbra]

okay i see...........

💔 this is so hard guys

i feel slow haahhahahahahhahahhhahhaa..a........... ARGRHRHH

[wintry gale]

I have to go now

I have classes for like 4 hours

I hope that sinks in though

[boreal umbra]

OK

GOODLUCK

THANKS

[night oak]

Strictly speaking, the basis of calculus is limits.

[wintry gale]

I’m back

[boreal umbra]

sorry it was three am for me 🥀

[boreal umbra]

why and what r limits

😨🫩

[balmy anchor]

Roughly speaking, we say that a function f approaches the limit l near a if we can make f(x) as close as we like to l by choosing x sufficiently close to a but unequal to a

This idea is followed by continuity, forming the basis of calculus

In this provisional definition of limits you can clearly see that what we've defined is not the word "limit", but the notion of "a function approaching a limit". That's how it is defined

A newbie mainly encounters smooth continuous everywhere functions in introductory calculus courses. For these type of functions limit near a certain point a is just f(a)

[uneven mirage]

ASR is Mathematicoid

[balmy anchor]

Although limits can be evaluated for these simple functions just by substituting the value of a in the function, this works only when the function is extremely simple. You have to learn how to evaluate limits when direct substitution yields "indeterminate forms" (Google it)

But if you try to find value of this limit directly

[night oak]

...no it doesn't.

[uneven mirage]

ASR is Mathematicoid

[night oak]

...no, it's not.

[balmy anchor]

I am showing what direct substitution looks like

[balmy anchor]

But actually, value of this limit is 1, not 0/0

[night oak]

Obviously it's not 0/0 because that doesn't exist.

[balmy anchor]

Not every limit does....

[heavy tendon]

@night oak even though you won't listen and @balmy anchor

Helper discussions in #helper-staff

[karmic bridge]

You ever wonder how speedometers work?

I'll.js wait till your here

[boreal umbra]

sorry i had school

hehe

[boreal umbra]

oh

so guys

i didnt understand

🥀

im actuals gona die

why is this concept so perplexable

[balmy anchor]

It seems confusing at first, just remember. When one mentions the word limit, they are actually talking about a function getting closer to some point, which they are calling the limit

[boreal umbra]

whats the significance of a limit tho

like how does it help

[hearty swift]

Hmm let's take a function sinx/x, tell me what it's value is at x=0

Or actually just refer to what the person before me said

[boreal umbra]

0

[hearty swift]

No

Do it again

And tell me everything you get

[boreal umbra]

🥀 okay

1

🥀

[hearty swift]

No rather than using desmos and everything do it yourself and tell me what you get

Sinx/x

Unless you've done limits you shouldn't get 1

[boreal umbra]

I DONT GET IT GUYS 🥀

so

do i like sub x=0 into sinx/x 🥀

idk how else ud do it

[hearty swift]

Yesss

[boreal umbra]

isnt sin of 0 just 0 🥀

[hearty swift]

Yep

[boreal umbra]

so isnt 0/0 just 0

[hearty swift]

And then what do you get?

[boreal umbra]

am i.. missing omehting guys 🥀

[hearty swift]

https://tenor.com/view/man-praying-black-man-praying-black-man-praying-and-crying-man-praying-and-crying-gif-23376408540985609

[boreal umbra]

STO

P

[hearty swift]

I wish it was

[boreal umbra]

WHAT I DONT GE IT

[hearty swift]

It isnt

[boreal umbra]

WAIT HOW

HOW

HOWOOWOWO

[hearty swift]

It's an inderminate form

[boreal umbra]

what 🥀

i feel tears inmy eyes

[hearty swift]

Division by 0 isn't possible

[boreal umbra]

oh right

uh

💔

GUYS

i swear

[hearty swift]

Bro forgor 💀

[boreal umbra]

its coz its coz um idk 🥀

guys im sorry.................................................

[hearty swift]

Yeah so like

[boreal umbra]

i just finished studying chemisty

yk how it is

🥀

[hearty swift]

You saw how x=0 gives 0/0 for sin/x

[boreal umbra]

ok so

non define

[boreal umbra]

yes

[hearty swift]

Now how do we find sinx/x at x=0 ?

[boreal umbra]

ummmm

uh

https://tenor.com/view/ugly-plankton-meme-ugly-plankton-ugly-face-plankton-meme-plankton-gif-15836444981074643801

guys idk

🥀

[hearty swift]

You use limits

Basically

Think abt it like this

[hearty swift]

You can't find something so you assume that what you are trying to find is between two values you can

[boreal umbra]

wait

u right

WAITTTTTTTT

WAITTTTTTTTTTTTTTTTTTTTTTTT THATS TRUE

[hearty swift]

Yeah so what we do for that is start approximating the value of sinx/x using the values of something larger and something smaller

Now rn I'm sleepy so I can't remember the exact method for sinx/x 😭😭😭

But it's a very basic and useful proof

It takes value 1 as you saw using desmos

[boreal umbra]

dw im worse twin

[boreal umbra]

yes desmos goat!

[hearty swift]

We're pretty much assuming that sinx/x doesn't do some stupid shit at x =0 when we take the limit

As far as I remember there is a method to check that

But I haven't read into it too deeply

[hearty swift]

True

[boreal umbra]

guys be honest am i cooked :wil

🥀

[hearty swift]

I mean how much time you got for calc?

[boreal umbra]

2 weeks

💔

ok but its only like

uh

not

[hearty swift]

What all are they asking you

[boreal umbra]

the entrie topic

[boreal umbra]

WIAT ill show u

[hearty swift]

Ok

[boreal umbra]

its chill right

right

[hearty swift]

Haven't done tangents since I found it boring rest everything will be pretty easy

[boreal umbra]

is tehre hope for someone like me .. 🙏

[hearty swift]

This is like 5% of the calc syllabus I have so yes

Yes there is

[boreal umbra]

REALLY

ill work hard guys trust

[hearty swift]

Yea there should be

[boreal umbra]

!!!!!!!!!!!!!!!!!!!!!111111111111111111

[hearty swift]

You should

Especially if you wish to score well

[boreal umbra]

bro liek coz everybody in my class gets tutoring 😨 so theyre already ahead

💔 i dont have allat

WHY am i singled out

so sad but its ok coz youtube and illegal websites r my best resources but its ok coz thats goa

t

[boreal umbra]

ok i will guys

swear on the water bill

anwyays what r u doing tho lowk

r u in uni

[hearty swift]

You could use mit resources they are free but idk if they cover these topics

[hearty swift]

School

[boreal umbra]

OMG yes i use mit

[boreal umbra]

secondary?

[hearty swift]

11th grade

[boreal umbra]

wait period

wait we lowkey twinning actually im in 9th tho

[hearty swift]

Idk what that is but I'm in 11th 😭😭

[boreal umbra]

im just accelerated ☹️

[hearty swift]

Oh

[boreal umbra]

but mentally im 11th trust

do u do chemistry

[hearty swift]

Dang I barely knew what calc was back in 9th

[hearty swift]

Yes

[boreal umbra]

period

[hearty swift]

Dealing with entropy rn

[boreal umbra]

SAME

wait technialy im doing entalpy

[hearty swift]

Lmao what are the chanced

[boreal umbra]

is that how u spell it

[hearty swift]

Enthalpy?

[boreal umbra]

yes

whoops..

[hearty swift]

Those are different sadly

[boreal umbra]

☝️

NOOOOOOOOOOOOOO

[hearty swift]

😥

[boreal umbra]

bro lowkey i might be cooked for chemistry too

everybody in my class is try hard

ok but that might bbe bc tehyre 11th graders but liek

💔

[hearty swift]

That is how I feel in my coaching/study Institute too

[hearty swift]

Even being there is good as is

[boreal umbra]

u right gang ☝️

dont tell anybody but i got 1 and 2 out of something onmy last two chemistry quizzes

🤫

[boreal umbra]

everybody is turning into newton ☹️

[hearty swift]

lmao maybe

i finally got some extra sleep in a long time

also getting back to the point, for the topics you showed to me id say 3b1b's calculus series of youtube is sufficient for the understanding part

[boreal umbra]

HUZZAH

[boreal umbra]

omg i know that gy

ok thanks

bro my firned told me to watch a 6 hr video of a guy differnetiating 💔 lowkey she might be onto somehting tho

[hearty swift]

name?

[boreal umbra]

UH let me find

blackpenredpen

https://www.youtube.com/watch?v=AegzQ_dip8k&t=843s

[hearty swift]

ohhhh this guy

makes sense

[balmy anchor]

@boreal umbra Did you get stuff

[hearty swift]

@boreal umbra (yea bro youre cooked today)

[balmy anchor]

Watching 100 football matches isn't making you Messi(perhaps)

[hearty swift]

https://tenor.com/view/realizing-2014-is-only-3-gif-12223818194305261467

ok i got class now

@karmic bridge

[karmic bridge]

Wsg vro

[hearty swift]

nothing just felt like annoying you

[wintry gale]

It’s him having fun rather than a learning expereince

You should watch his educational videos, rather

[boreal umbra]

💔 what does that men

OH sorry i didnt reply

but

okay

ummm 🥀

[hearty swift]

Js watch the videos where he actually explains what he is doing

He's taking abt bprp

[hearty swift]

This guy

[wide wigeon]

Yeah, bprp main channel usually consists of interesting but higher level problems. His alt channel named bprp calc basics however may be a good resource

Professor Dave Explains is also great at packing a lot into a small timeframe while keeping it easy to follow: https://youtube.com/playlist?list=PLybg94GvOJ9ELZEe9s2NXTKr41Yedbw7M&si=GewTH8Vpu8oRPk12

I know 35 videos seems like a lot but that playlist has basically all the calculus you’d learn in a 2 year time frame in high school

[boreal umbra]

OKAY THANKS BRO

🙏

[little mantle]

cooked

[boreal umbra]

🥀🥀🫩

dont needa remind me

[arctic creek]

@boreal umbra

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[gleaming crescent]

What's going on gng you get the concept of limits?

[hardy thorn]

It's much easier than it sounds

TLDR; Limits are a way to determine values that don't necessarily exist on a graph. Imagine the graph of the natural logarithm

You cant say that 0 exists on the graph but you DO notice that it APPROACHES 0 on the x-axis

So we can write that
limit of x-> 0 = negative infinity

This will be useful when you analyze graphs and models, and do regression with this knowledge

[night oak]

No, that's backwards.

[hardy thorn]

Oh sorry ill edit

My fever is messing with my abilities to exist