Calculus

[neat granite]

how to solve pliz help

[soft crypt]

wym how to solve ?

it's just computing derivatives

(although there's smarter ways than others here)

@neat granite

[neat granite]

yeah i basically need that smarter way

[soft crypt]

do you have an answer already

even if it's not found in a smart way

[soft crypt]

focus on u * du/dx for a minute, it looks familiar eh
it's almost d(u^2)/dx

[neat granite]

bro i can't get u

[soft crypt]

d(u^2)/dx = 2 u * du/dx is my point

same for v

so u * du/dx = 1/2 d(u^2)/dx

turns out that simplifies a whole lot of stuff here

[neat granite]

can u pliz show me?

[soft crypt]

show what ?

[neat granite]

i did till second order derivative but not able to get the answer

[neat granite]

ur step

in a paper coz i can't get u

[soft crypt]

$$\dv{(u^2)}{x} = u \dv{u}{x} + \dv{u}{x} u = 2u\dv{u}{x}$$

[neat cargo]

aPlatypus

[soft crypt]

@neat granite

[neat granite]

bro is dis a formula?

[soft crypt]

yeah

it's just product rule

u^2 = u * u

[neat granite]

oh i c

[soft crypt]

so $u\dv{u}{x} = \frac12 \dv{(u^2)}{x}$

[neat cargo]

aPlatypus

[soft crypt]

same for $v$, $v\dv{v}{x} = \frac12 \dv{(v^2)}{x}$

[neat cargo]

aPlatypus

[soft crypt]

try and add those

[neat granite]

ok until den can u help me with this as well?

[soft crypt]

sure

let's just finish the first though

[neat granite]

ok

[soft crypt]

^

@neat granite

[neat granite]

got stucked at 1 step

[soft crypt]

yeah?

[neat granite]

Wt to do after dis?

[soft crypt]

you don't have to compute them seperately

alright I'll spell it out completely for you

\begin{align*}
u\dv{u}{x} + v\dv{v}{x} &= \frac12 \dv{(u^2)}{x} + \frac12 \dv{(v^2)}{x} \\
&= \frac12 \dv{(u^2 + v^2)}{x}
\end{align*}

[neat cargo]

aPlatypus

[soft crypt]

that 2nd line works cause the derivative is a linear operator

df/dx + dg/dx = d(f+g)/dx

[neat granite]

bro can we do coding here?

[soft crypt]

nah this bot is only a thing that types math

[neat granite]

oh

[soft crypt]

now u^2 + v^2 is easy to work with

[neat granite]

still need to use uv form ryt?

[soft crypt]

it's just e^(2ax)

[neat granite]

The final asnwer?

[soft crypt]

no

u^2 + v^2 is e^(2ax)

[neat granite]

Formula?

[soft crypt]

no?

literally from the functions you are given

but I mean honestly if you have trouble with your algebra, I'd focus on getting better at algebra before using fancy tricks like I'm doing here

[neat granite]

Bro i think there is a mistake in ur step

[soft crypt]

if your algebra is already shaky, you just won't notice the trick

[soft crypt]

ok which one ?

[neat granite]

it should be 2e^2ax ryt?

as sin^2bx+cos^2bx gives 1

[soft crypt]

nope

e^(2ax) cos^2(bx) + e^(2ax) sin^2(bx) = e^(2ax) * (cos^2(bx) + sin^2(bx)) = e^(2ax) * 1

algebra again mate

[neat granite]

bro i can't get that step

did u jump any step?

[soft crypt]

it's just factoring

[neat granite]

how dis step came from 1/2d(u^2+v^2)?

[soft crypt]

I'm not even talking about the derivative yet

just u^2 + v^2

@neat granite

[neat granite]

did u use uv?

[soft crypt]

wdym ?

no I'm not using product rule

just straight up algebra

[neat granite]

ok got it

[soft crypt]

alright so u^2 + v^2 = e^(2ax)

that's quite easy to find the derivative of that

\begin{align*}
u\dv{u}{x} + v\dv{v}{x} &= \frac12 \dv{(u^2)}{x} + \frac12 \dv{(v^2)}{x} \\
&= \frac12 \dv{(u^2 + v^2)}{x} \\
&= \frac12 2ae^{2ax} \\
&= ae^{2ax}
\end{align*}

[neat granite]

got it bro

[neat cargo]

aPlatypus

[neat granite]

thanks a lot

[soft crypt]

but yeah get your algebra straight though

you won't have me for your test

[neat granite]

u just said algebra so i was wondering where did the functions go

but u used trigo too

[soft crypt]

if your algebra isn't perfectly fine, you won't notice those tricks

[neat granite]

bro how can i improve?

[soft crypt]

khan academy is prolly fine

[neat granite]

i did till second order derivative but not able to get the answer

[soft crypt]

yeah what are the derivatives you got ?

[neat granite]

xy' = cos(logx)

xy''={-sin(logx)}/x

where r u from btw bro?

[soft crypt]

europe

your derivatives are fine

[neat granite]

cool bro

[soft crypt]

that question seems screwed up indeed

if anything x^2 d^2y/dx^2 + y = 0 works

,w solve y'' + y = 0

[neat cargo]

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[soft crypt]

,w solve y'' = 0

[neat cargo]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by _aplatypus

[soft crypt]

,w solve x^2y'' + xy' + y = 0

[neat cargo]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by _aplatypus

[soft crypt]

oops, should have talked more slowly I guess

[neat granite]

y bro

sorry if i did anything wrong i'm new to discord

bro u there?

[soft crypt]

yeah

your second derivative doesn't work now that I think about it

[neat granite]

wt was this?

[soft crypt]

xy' = cos(logx)
xy''={-sin(logx)}/x
the 2nd one doesn't follow from the first

[neat granite]

it does bro

[soft crypt]

I said that the question was screwed up when it wasnt

[soft crypt]

nope

you differentiated both sides

however on the right side there's a product of two functions

[neat granite]

y' is {cos(logx)}/x

[soft crypt]

ok sure

[neat granite]

now to differentiate again i took x to left hand side

[soft crypt]

you can just differentiate like that

but ok you can try by putting x to the LHS

[neat granite]

how bro

quotient rule?

[soft crypt]

yes

your way isn't bad either

you screwed up the execution that's all

xy' = cos(log(x))

[neat granite]

i did according to options😭

[soft crypt]

so d/dx (xy') = d/dx (cos(log(x)))

on the right you get -sin(log(x))/x indeed

on the left you have a product of two functions

xy'' + y' = -sin(log(x))/x

x^2 y'' + xy' = -sin(log(x))

that's a valid deduction

[neat granite]

bro in quotient rule i think it went more hectic

[soft crypt]

yeah it's a bit harder

[soft crypt]

this is fine though

so x^2 y'' + xy' + y = -sin(log(x)) + sin(log(x)) = 0

[neat granite]

ohh

so wt to do from here bro

[soft crypt]

your 4th line is wrong

that's what I've been saying for the past 10 minutes

[neat granite]

how bro

[soft crypt]

xy' is a product of two functions

you can't just say the derivative of xy' is xy''

as attractive as it sounds

[neat granite]

in the option they gave this way only ryt?

[soft crypt]

I solved it already

[soft crypt]

wdym it's in the options

[neat granite]

the option c

[soft crypt]

if you do a wrong step you'll get fucked up results that's all I'm saying

[neat granite]

bro literally i'm not getting ur steps

[soft crypt]

you won't get option c with the way you've done it

[neat granite]

can u pliz use pen and paper?

[soft crypt]

$$\dv{(xy')}{x} = \dv{x}{x}y' + x\dv{(y')}{x} = y' + xy''$$

[neat cargo]

aPlatypus

[soft crypt]

product rule

@neat granite

[neat granite]

hmm let me try to work it out once now

are these correct?

[soft crypt]

$$\dv{(xy')}{x} = \cos(\log(x)) - \sin(\log(x))$$

[neat cargo]

aPlatypus

[soft crypt]

yes that's true

your notations are completely wtf though

but it seems like you got it

[neat granite]

wt to do after these now

[neat granite]

so basically these is my y'' ?

but i was solving y'' only ryt?

[soft crypt]

wait nvm

xy' is already cos(log(x))

[echo fern]

want me to continue? @soft crypt

[soft crypt]

ig

[neat granite]

i'm ok with that too

y'' ki baat ho rahi hai bhai

haan

hmm

hm

haan

wahi pe product rule lagaya

[neat granite]

ye

lhs and rhs ko alag se calculate karni hai?

dekho jo mera y' hai wo cos(log(x)) hai na?

to maine x*cos(log(x))/x kiya

kyu ki wahi mera y' tha

[neat cargo]

Dissrupt

[neat granite]

yes

bhai ek paper notebook mai samjhado na

oo

abhi tak to aya

[neat granite]

x *y' kiya

[neat granite]

Bhai sorry internet server down ho gaya tha

@echo fern kya tum ho?

Fir ye aaya

Bhai dy/dx cos{log(x)} /x aya ryt

Fir x ko left hand side bhej diya

X*dy/dx=x cos{log(x)} ryt?

Kyu ki mere dy/dx hi toh cos( log( x)/x hai

Bhai come straight to the point

Kaha galti kiya wo batao

Wiase tum kaha se ho bhai

Itna badiya hindi bol rahe ho

[neat cargo]

Dissrupt

[neat granite]

Haan yehi toh maine bhi kiya tha

Matlab(a+b) ²= a²+b²+2ab aisa nahi hai ye

Rhs lhs ka result nahi dega?

Wo toh maine bas example diya tha identity ka

Like rhs is not the result of lhs ye kehna chahte ho ryt?

Y kya hai?

Y =Sin (log(x)) na?

Bhai maine kaha galti kiya wo step batao na

Y ka value put nahi karna hai?

Ok in general ki baat kar rahe ho

Like derivative of dy/dx is d²y/dx²?

1 ayega

Okok

[neat cargo]

Dissrupt

[neat granite]

Abhi rhs ko bhi alag se differentiate karna hai?

[neat granite]

Got it

Product rule rhs mai bhi?

Rhs ka equation batana ekbar

Den - sin(log(x) /x

Sahi hai?

X²d²y/dx² +xdy/dx=- sin(log(x)?

Sin (log(x))

Lhs jane se y ban jayega ok

Got it

Thansk a lot

Haan bhai

Kaha se ho tum?

Maine bich se hi options ke saath match karne ki koshis ki isliye

Konsi state?

Achi baat hai Indian bhi calculus chat mai hi kr pa rahe hai

Bhai wo dusra bhai jo tha wo tumhara dost hai?

Tum phone nahi chalate?

Konsi class mai ho tum?

Oo cbse?

Pass out iss saal

Lekin bas naam ka

11 aur 12 covid mai chala gaya

Nah

Lekin manipur mai violence ho raha hai na

Isliye dadi ke ghar mai baitha hu

Algebra strong karo bol raha tha woh bhai

Kya chij strong karna hai exactly

Tumse pahele jo mukhe sikha raha tha

Haan

Yes

Lekin ab realise huwa 12 ka 20% bhi cover nahi kya hamare time mai

Nahi manipur mai hi jaakr karunga

Waise distance course lene ka soch raha hu

Abhi toh mere pass kitan nahi hai 11 ka

Pata nahi jo option milega usi ka lelunga bas degree ke liye

Toh kaha se padu bhai?

Waise woh derivative bot ko chalana sikha do na

Integration bhi hoga usse?

Kaha se?

Youtube pe nahi milenge?

Waise ncert se nahi toh kaha se padu?

Yehi bots ko chalane ka tarika

Konsi channel se?

Latex matlab?

Aaj hi naam sun rahu hu bhai

Famous nahi hai woh?

Lekin mai jee ke liye preparation nahi kar rahu hu

Wahi basic hi hila hai bhai

Corona ke time mai 11 ka pura online hi huwa

Aur 12 mai bhi maths maam ne school lately join kiya

Integration ka out of 11 exercise bas 5 the

Yh?

Oh yt bolo na

Ok

Thanks bhai

Abhi nda ka pyqs tha wo question

Ohh

Maine first time encounter kiya

Like jo general derivative hai us ka question aj tak nahi kiya tha

Isliye kuch nahi samaj mai ah raha tha

Oh

Bas 1 months baki hai ab🥶

Nda sept 3 ko hai

Isliye to pyqs kar raha tha

11th?

Sukriya

Nah nah nahi karunga

Abhi toh bas pyqs hi karta jaunga

Kaha pe?

.solved

Oo

Acha case sensitive hai🤣

Ho gaya?

.solved

[inner salmon]

Solved

Post marked as solved by @neat granite.

Use .unsolved if this was a mistake.

[neat granite]

Ok itna advanced badiya

@soft crypt how shall i search algebra basics or algebra for calculus?

[soft crypt]

if you want a book, there's basic mathematics by serge lang which is quite alright for that (findable online not too difficultly)

if you prefer online, review the algebra part in khan academy, at least you have an infinite source of exercises there (although repetitive)

[neat granite]

Algebra covers exponents and?

[soft crypt]

I just put basic computation in algebra in my head (i'm a bit old lol)

I guess precalculus would be more fitting to your needs rn

[neat granite]

Wts precalculus?

[soft crypt]

https://en.wikipedia.org/wiki/Precalculus

[neat granite]

I'm ok with trigo

[soft crypt]

it's a bit of a melting pot of algebra and common functions (trig, log, exponential, ...non-exhaustive list)

[neat granite]

Oh