
Portuguese: 
Digamos que temos y igual a
cosseno de cinco x menos três y,
e que o que quero é encontrar
a taxa com que y varia com relação à x,
assumindo que y é função de x.
Vamos então fazer o que fizemos até agora,
vamos aplicar o operador diferencial
em ambos os lados dessa equação.
No lado esquerdo da equação, aqui,
temos dy/dx igual a -
agora no lado direito
vamos aplicar a regra da cadeia.
A derivada do cosseno de alguma coisa
com relação a ela mesma será igual a
menos o seno dessa coisa. Então menos 
seno de cinco x menos três y
e então temos que multiplicar isso pela 
derivada daquela coisa em relação a x.
Qual a derivada disso
com relação a x?
A derivada de cinco x com relação
a x é cinco,

Georgian: 
მოდით ვთქვათ, რომ გვაქვს: y=cos(5x-3y)
და რისი პოვნაც მინდა, არის კოეფიციენტი, რომლის y-იც იცვლება x-ის მიხედვით
და დავუშვათ, რომ y არის ფუნქცია x-ის.
მოდით გავაკეთოთ, რასაც ყოველთვის ვაკეთებდით.
გამოვიყენოთ წარმოებული ამ განტოლების ორივე მხარეს.
განტოლების მარცხენა მხარეს, აქ, მივიღეთ dy/dx= ...
ახლა აქ მარჯვენა მხარეს გამოვიყენოთ ჯაჭვური პრინციპი.
კოსინუსის წარმოებული, რაღაც რიცხვზე დამოკიდებული ტოლი იქნება ამ რიცხვის მინუს სინუსის ტოლი.
უარყოფითი სინუსი -(5x-3y)-ის
და შემდეგ უნდა გავამრავლოთ წარმოებულ რიცხვზე, რომელიც იცვლება x-ის მიხედვით.
რა არის ამ რიცხვის წარმოებული x-ის მიხედვით?
წარმოებული 5x-ის x-ის მიხედვით არის 5

Chinese: 
比如说我们有这样一个关系式
y等于

Thai: 
สมมุติว่าเรามีความสัมพันธ์ y เท่ากับโคไซน์ของ 5 x ลบ 3 y
แล้วสิ่งที่ผมอยากหาคืออัตราที่ y เปลี่ยนแปลงเทียบกับ x
และเราสมมุติว่า y เป็นฟังก์ชันของ x
ลองทำสิ่งที่เราเคยทำมากัน
ลองใช้ตัวดำเนินการอนุพันธ์ทั้งสองข้างของสมการนี้
ทางซ้ายมือ, ตรงนี้, เราได้ dy/dx เท่ากับ
ตรงนี้ทางขวามือ เราจะใช้กฎลูกโซ่
อนุพันธืของโคไซน์อะไรสักอย่าง เทียบกับอะไรสักอย่างนั้น เท่ากับลบ ไซน์ของตัวนั้น
ได้ ลบ ไซน์ของ 5 x ลบ 3 y
แล้วเราก็คูณมันด้วยอนุพันธ์ของอะไรสักอย่างนั่นเทียบกับ x
แล้วอนุพันธ์ของอะไรสักอย่างนั้นเทียบกับ x คืออะไร?
ทีนี้อนุพันธ์ของ 5x เทียบกับ x ได้ 5

English: 
Let's say we have
the relationship
y is equal to cosine
of 5x minus 3y.
And what I want to find
is the rate at which y
is changing with respect to x.
And we'll assume that
y is a function of x.
So let's do what we've
always been doing.
Let's apply the
derivative operator
to both sides of this equation.
On the left-hand
side, right over here,
we get dy/dx is equal to-- now
here on the right hand side,
we're going to apply
the chain rule.
The derivative of the
cosine of something,
with respect to
that something, is
going to be equal to negative
sine of that something.
So negative sine of 5x minus 3y.
And then we have
to multiply that
by the derivative of that
something with respect to x.
So what's the derivative of the
something with respect to x?
Well the derivative of
5x with respect to x
is just equal to 5.

Czech: 
Řekněme, že máme vztah
y rovná se cos(5 krát x minus 3 krát y).
Chceme spočítat, jaká je
rychlost změny y vzhledem k x,
přičemž předpokládáme,
že y je funkcí proměnné x.
Udělejme to,
co vždycky děláme,
tedy použijme na obě strany
rovnice operátor derivace.
Na levé straně nám vyjde
dy lomeno dx, což se rovná...
Na pravé straně použijeme
vzorec pro derivaci složené funkce.
Derivace kosinu něčeho podle toho něčeho
se rovná minus sinus toho něčeho.
Tedy minus
sin(5 krát x minus 3 krát y),
což ještě musíme vynásobit
derivací onoho něčeho podle x.
Jaká je tedy derivace
našeho něčeho podle x?
Derivace z (5 krát x)
podle x je 5

Bulgarian: 
Нека да приемем, че 
е дадена зависимостта
y е равно на косинус от (5x – 3y).
Искам да намеря,
скоростта, с която y
се изменя спрямо x.
Ще предположим, че y е функция на x.
Нека да направим това, което 
винаги сме правили.
Нека да запишем означението за производна d/dx
в двете страни на уравнението.
От лявата страна, точно ето тук,
получаваме dy/dx е равно на...
Сега тук от дясната страна
ще приложим верижното правило.
Производната на косинус от нещо
спрямо това нещо,
ще бъде равна на 
минус синус от това нещо.
Тоест минус синус от (5x – 3y).
След това трябва да умножим това
по производната на този израз
спрямо x.
А каква е производната на 
този израз спрямо x?
Производната на 5x спрямо x
e равна просто на 5.

Tamil: 
 
இப்படி நாம ஒரு தொடர்பை பர்க்கலாம்.
அது y சமம் cos (காஸ்)அடைப்பு 5x கழித்தல் 3y என்பதாகும்.
நம்ப என்ன கண்டுபிடிக்க வேண்டுமென்றால் எந்த மதிப்பிற்க்கு
xஐ பொறுத்து y மாறுபடுகிறது என காண வேண்டும்.
இப்பொழுது நாம் வைத்துக் கொள்வது என்னவென்றால்
y என்பது x ஐ சார்ந்திருக்கும்.
அடுத்ததாக செய்ய வேண்டியது
இரண்டு புறமும் வகைபடுத்த வேண்டும்.
இப்பொழுது இடது பக்கம் xஐ பொறுத்து வகைபடுத்தினால்
கிடைப்பது dy/dx என்பதாகும். வலது பக்கத்தில்
செய்வதற்கு சங்கிலி விதியை பயன்படுத்த வேண்டும்.
முதலில் cosine விகிதத்தை வகைபடுத்தினால்
நமக்கு கிடைப்பது எதிர்குறி கொண்ட sin(-sin) என்பதாகும்.
ஆகவே cos அடைப்பு 5x கழித்தல் 3yஐ வகைபடுத்தும் போது
கிடைப்பது -sin/5x கழித்தல் 3y
பிறகு பெருக்கலில் உள்ளவற்றில்
முதலாவதாக உள்ள 5x ஐ
xஐ  பொருத்து
வகையீடு செய்தால்
நமக்கு கிடைப்பது 5 ஆகும்.

Turkish: 
Diyelim ki y eşittir kosinüs 5 x eksi 3 y bağıntısı var.
Ve y'nin x'e göre değişim hızını bulmak istiyorum.
y'nin x cinsinden bir fonksiyon olduğunu varsayıyorumç
Şimdi her zaman yaptığımız şeyi yapalım ve iki tarafın türevini alalım.
-
Sol tarafta d y d x alacağız.
Sağ tarafta da zincir kuralını uygularız.
Bir ifadenin o ifadeye göre kosinüsünün türevi eşittir o ifadenin eksi sinüsü.
Yani eksi sinüs 5 x eksi 3 y.
Sonra da bunu o ifadenin x'e göre türeviyle çarparız.
Bu ifadenin x'e göre türevi nedir?
5 x'in x'e göre türevi eşittir 5 ve eksi 3 y'nin x'e göre türevi eşittir eksi 3 çarpı d y d x.

Korean: 
 
다음 식을 살펴봅시다
y = cos(5x-3y)
우리는 y의 x에 대한
변화율을 구하고자 합니다
y가 x에 대한 함수라고 하죠
우리가 항상 하던 것을 해봅시다
양변에 미분연산자를 써볼게요
양변에 미분연산자를 써볼게요
좌변은
dy/dx가 되고, 우변에서는
체인룰을 써보죠
cos(5x-3y)의
5x-3y에 대한 미분은
-sin(5x-3y)이 되죠
-sin(5x-3y)이 되죠
그리고서는 여기에
5x-3y의 x에 대한 미분을 곱합니다
5x-3y의 x에 대한 미분을 구하면
5x의 미분은
5가 되고

Georgian: 
და წარმოებული -3y-ის x-ის მიხედვით არის -3*dy/dx.
-3-ჯერ y-ის წარმოებული x-ის მიხედვით
და ახლა გვჭირდება, რომ ვიპოვოთ dy/dx.
როგორც ხედავთ, მოცემულია განსხვავებული ცვლადები, ეს არის რთული ნაწილი.
ნა,დვილად, ნება მომეცით გავაკეთო ეს dy/dx იგივე ფერში, ასე უფრო ადვილია.
ეს იქნება dy/dx და შემდეგ შემიძია დავხურო ფრჩხილები.
როგორ შეგვიძლია ამის გაკეთება? ცოტა ალგებრული სამუშაო გვექნება.
შეგვიძლია გავანაწილოთ (5x-3y)-ის სინუსი, ნება მომეცით გადმოვწერო ყველაფერი.
შეგიძიათ გაანაწილოთ (5x-3y)-ის სინუსი - მიიღებთ, ნება მომეცით გადმოვწერო ყველაფერი. მიიღებთ dy/dx. ანაწილებთ მინუს სინუსს, გექნებათ 5x-3y.

English: 
And the derivative of
negative 3y with respect to x
is just negative 3 times dy/dx.
Negative 3 times the derivative
of y with respect to x.
And now we just need
to solve for dy/dx.
And as you can see, with some of
these implicit differentiation
problems, this is the hard part.
And actually, let me make
that dy/dx the same color.
So that we can keep
track of it easier.
So this is going to be dy/dx.
And then I can close
the parentheses.
So how can we do it?
It's just going to be a little
bit of algebra to work through.
Well, we can distribute
the sine of 5x minus 3y.
So let me rewrite everything.
We get dy-- whoops, I'm going
to do that in the yellow color--
we get dy/dx is equal
to-- you distribute
the negative sine
of 5x minus 3y.
You get-- so let me make sure
we know what we're doing.
It's going to be, we're
going to distribute that,
and we're going to
distribute that.
So you're going to have
5 times all of this.

Portuguese: 
e a derivada de menos três y com 
relação a x é menos três vezes dy/dx.
Menos três vezes a derivada de y
com relação a x.
Agora é só resolver para dy/dx.
Como você pode ver, a parte difícil são
essas problemas diferenciais implicitos.
Deixe-me colocar dy/dx na mesma cor
para que possamos seguí-lo melhor.
Então esse será dy/dx, e agora posso
fechar os parênteses.
O que fazer? Teremos que usar
um pouco de álgebra.
Podemos distribuir o seno de cinco x
menos três y - deixe-me reescrever -
Teremos dy/dx é igual a - você distribui
menos seno de cinco x, menos três y e terá
Deixe-me certificar sobre o que estamos 
fazendo: distribuímos aqui e aqui.

Turkish: 
-
Eksi 3 çarpı y'nin x'e göre türevi.
Şimdi d y d x'i bulacağız.
Genelde kapalı fonksiyon türevlerinde bu kısım zor olur.
d y d x 'i aynı renk yazayım ki daha rahat işlem yapabilelim.
Bu d y d x olacak ve parantezi kapatıyorum.
Bunu nasıl bulacağız? Cebirsel işlemler gerekecek.
Sinüs 5 x eksi 3 y'yi dağıtabilirim. Baştan yazayım.
Eksi 5 sinüs 5 x eksi 3 y'yi dağıtıyoruz, yani eksi 5 çarpı sinüs 5 x eksi 3 y ve sonra eksi çarpı eksi.

Tamil: 
அடுத்ததாக xஐ பொருத்து கழித்தல் y ஐ வகையீடு
செய்தால் நமக்கு கிடைப்பது கழித்தல் 3 dy/dx என்பதாகும்.
dy/dx சமம் கழித்தல் sin அடைப்பு 5x கழித்தல் 3y அடைப்பு 5-3 dy/dx என்பது கிடைக்கும்.
மேலும் இன்னமும் முழுமையான வகைகெழு
நாம செய்யவில்லை. இனி வருவது கொஞ்சம் கடினமான பகுதி.
அதனால இருபுறமும் உள்ள dy/dx ஐ
நான் ஒரே வண்ணமாக மாற்ற போகிறேன்.
இப்ப என்ன பண்ணறுமுனா
அடைப்பு குறிகளை நீக்க வேண்டும்.
அதை எவ்வாறு செய்வது? மிகவும்.
எளிது இயற்கணித பாடத்தில்
படித்திருப்பது போலவே செய்ய வேண்டும்.
இப்ப sin அடைப்பு 5x கழித்தல் 3y  ஐ நான் பங்கிடபோறேன் இப்ப எல்லாவற்றையும் மீடும் திருபி எழுதுவோமா? சரி எழுதியாச்ச.
நாம dy/dn ஒரே பக்கமாக கொண்டு வருவதற்காக
இதை தனிதனியாக பிரிக்க போகிறோம்.
என்பதை நன்றாக புரிந்து கொள்ள வேண்டும்.
இப்பொழுது கழித்தல் sin
அடைப்பு 5x கழித்தல் 3y ஐ
முதலில் 5 ஆல்
பெருக்கினால் கிடைப்பது
கழித்தல் 5 sin

Korean: 
-3y의 x에 대한 미분은
-3dy/dx가 되겠죠
즉, y의 x에 대한 미분에 -3배입니다
이제 dy/dx에 대해 정리하면 됩니다
일부 문제에서는
이것이 어려운 부분입니다
그 전에 dy/dx를 같은 색으로 쓸게요
더 잘 보이게 말이죠
 
그리고 괄호를 닫을게요
이제 어떻게 할까요
사실 그냥 단순한 대수학입니다
우선, sin(5x-3y)를 분배합시다
전체 식을 다시 쓸게요
dy/dx는
dy/dx는
-sin(5x-3y)를 분배한 것,
그림으로 표현하자면
다음과 같이 됩니다
다음과 같이 됩니다
식을 쓰면 -sin(5x-3y)의 5배

Bulgarian: 
А производната на –3y спрямо x
е просто минус 3 по dy/dx.
Минус 3 по производната на y спрямо x.
Сега просто трябва да решим 
уравнението за dy/dx.
Както можеш да видиш, 
при някои от тези задачи
за неявно диференциране
това е трудната част.
И всъщност, нека да направя това
 dy/dx в различен цвят,
Така че да може да го следим по-лесно.
Това ще бъде равно на dy/dx.
И сега мога да затворя скобите.
Как може да го решим?
Просто ще използваме малко алгебра 
в този процес.
Може да разкрием скобите за
синус от (5x – 3y).
Нека да запиша отново всичко.
Получаваме dy...
Ще направя това в жълт цвят.
Получаваме, че dy/dx е равно
 на... Разкриваме скобите и умножаваме по
минус синус от (5x – 3y).
Нека да се уверя, 
че знаем какво правим.
Ще се получи...
ще умножим по този член
и ще умножим по другия член.
Ще получиш 5 по всичко това.

Czech: 
a derivace z (−3 krát y) podle x
se rovná −3 krát (dy lomeno dx),
tedy −3 krát
derivace y podle x.
Nyní musíme osamostatnit
dy lomeno dx.
Jak můžete vidět i v jiných
úlohách na implicitní derivování,
teď přichází
ta nejtěžší část.
dy lomeno dx udělám stejnou barvou,
abych lépe viděl, kde je mám.
Tady je tedy
dy lomeno dx.
Ještě musím
uzavřít závorku.
Jak to teď
uděláme?
Budeme se teď muset
prokousat trochou algebry.
Můžeme roznásobit
sinem z (5 krát x minus 3 krát y).
Všechno to přepíšu.
Dostaneme, že dy...
Ouha, chtěl bych to
mít tou žlutou barvou.
Dostaneme, že
dy lomeno dx se rovná...
Když roznásobíme minus sinem
z (5 krát x minus 3 krát y), dostaneme...
Ještě ujasním,
co tu děláme.
Vynásobíme to tímhle
a pak tímhle.

Thai: 
อนุพันธ์ของลบ 3y เทียบกับ x เท่ากับ ลบ 3 คูณ dy/dx
ลบ 3 คูณอนุพันธ์ของ y เทียบกับ x
ทีนี้เราก็ต้องแก้หา dy/dx
อย่างที่คุณเห็นในปัญหาเรื่องการอนุพันธ์โดยนัย, นี่คือส่วนที่ยาก
ที่จริงขอผมใช้ dy/dx เป็นสีเดียวกันดีกว่า, เราจะได้ตามดูมันได้ง่ายๆ
นี่จะเท่ากับ dy/dx แล้วผมก็ปิดวงเล็บ
แล้วเราจะทำอย่างไรดี? มันต้องคิดพีชคณิตนิดหน่อย
เราสามารถกระจายไซน์ของ 5x ลบ 3y ได้. งั้นขอผมเขียนทุกอย่างใหม่
คุณกระจายไซน์ของ 5x ลบ 3y -- คุณจะได้, ขอผมเขียนใหม่หมดเลยนะ. คุณจะได้ dy/dx. คุณกระจายลบไซน์เข้าไป, คุณจะได้ 5x ลบ 3y

Czech: 
Dostaneme 5 krát tohle, tedy
−5 krát sin(5 krát x minus 3 krát y),
a potom minus krát
minus nám dá plus,
takže to bude plus 3 krát sin(5 krát x
minus 3 krát y) krát (dy lomeno dx).
Nyní můžeme od obou stran odečíst
3 krát sinu z (5 krát x minus 3 krát y).
Aby bylo jasno, tak tohle
je 1 krát dy lomeno dx,
takže když tohle odečteme
od obou stran, zbyde nám...
Na levé straně máme
jedno dy lomeno dx
a od toho odečteme 3 krát sin(5 krát x
minus 3 krát y) krát (dy lomeno dx),

Bulgarian: 
Ще получиш минус това 5 по
синус от (5x – 3y).
След това ще получиш минус по минус,
така че накрая ще се получи плюс.
Накрая ще получиш плюс 3 по
синус от 5x минус 3y по dy/dx.
Сега може да извадим 3 по 
синус от (5x – 3y)
от двете страни на уравнението.
За да изясним, това е просто 1 по dy/dx.
Ако извадим този израз от 
двете страни, ще получим следното.
От лявата страна 
ще се получи 1 по dy/dx
и от него ще извадим израза 
3 по синус от (5x – 3y) по dy/dx.

Tamil: 
அடைப்பு 5x கழித்தல்
3y.
பிறகு நாம கழித்தல் sin அடைப்பு 5x கழித்தல் 3y ஐ
கழித்தல் 3 dy/dx  உடன் பெருக்க வேண்டும்.
முதலில் இரண்டு குறைகுறிகளை பெருக்கினால் கிடைப்பது மிகை குறி ஆகும்.
பிறகு 3 dy/dx ஆல் பெருக்கினால்
 
3sin  அடைப்பு
5x கழித்தல் 3y dy/dx நமக்கு கிடைக்கும்.
தற்பொழுது இடதுபக்கமாகவும்,
வலதுபக்கமாகவும் உள்ள
dy/dx ஒரே பக்கமாக கொண்டு
வர வேண்டும். வலது பக்கத்தில் உள்ள
3 sin அடைப்பு 5x கழித்தல் 3y

Thai: 
ทั้งหมดนี้, คุณจะได้ ลบ 5 คูณไซน์ของ
5x ลบ 3y แล้วคุณจะได้ ลบ คูณลบ
คุณจะได้บวก แล้วคุณจะได้ บวก 3
คูณไซน์ของ 5x ลบ 3y
dy/dx
ทีนี้สิ่งที่เราทำได้คือ ลบ 3 ไซน์ของ 5x ลบ 3y จากทั้งสองข้าง
นี่ก็คือ 1 dy/dx
แล้วถ้าเราเลบนี่จากทั้งสองข้าง เราจะเหลือ
ทางซ้ายมือจะเป็น 1 dy/dx
แล้วเราลบมันจาก 3 ไซน์ของ 5x ลบ 3y dy/dx

Georgian: 
გექნებათ -5 გამრავლებული (5x-3y)-ის სინუსზე
და შემდეგ გექნებათ უარყოფით-ჯერ უარყოფითს.
დაამთავრებთ დედბითით და გექნებათ
3-ჯერ (5x-3y)-ის სინუსზე
dy/dx
ახლა შეგვიძლია გამოვაკლოთ 3sin(5x-3y) ორივე მხარეს.
ეს არის dy/dx.
თუ გამოვაკლებთ ამას ორივე მხარეს, დაგვრჩება...
მარცხენა მხარეს გვაქვს dy/dx
და ვაპირებთ გამოვაკლოთ 3sin(5x-3y) dy/dx's

English: 
So you're going to have
negative this 5 times
the sine of 5x minus 3y.
And then you're going to have
the negative times a negative,
those are going to, you're
going to end up with a positive.
And so you're going to
end up with plus 3 times
the sine of 5x minus 3y dy/dx.
Now what we can do
is subtract 3 sine
of 5x minus 3y from both sides.
So just to be clear, this
is essentially a 1 dy/dx.
So if we subtract this from
both sides, we are left with--
So on the left-hand side,
we're going to have a 1 dy/dx,
and we're going to subtract
from that 3 sine of 5x minus 3y
dy/dx's.

Portuguese: 
Então cinco vezes tudo isso, teremos menos
cinco vezes seno de cinco x,
menos três y, e então você terá negativo
vezes negativo, portanto positivo,
então temos mais três vezes o 
seno de cinco x menos três y, dy/dx.
Agora, podemos subtrair três seno de 
cinco x menos três y de ambos os lados.
Para que fique claro, isso é
um dy/dx.
Então se subtrairmos isso de ambos os
lados, teremos:
no lado esquerdo, teremos um dy/dx,
e iremos subtrair três seno de cinco x
menos três y dy/dx dele

Turkish: 
-
-
Bu, artı olur. Artı 3 çarpı sinüs 5 x eksi 3 y d y d x.
-
-
İki taraftan 3 sinüs 5 x eksi 3 y'yi çıkarırız.
Bu aslında 1 d y d x.
Bunu iki taraftan çıkarırsak, sol tarafta 1 d y d x'ten 3 sinüs 5 x eksi 3 y d y d x'i çıkarıyoruz.
-
-

Korean: 
즉, -5sin(5x-3y)가 되고
즉, -5sin(5x-3y)가 되고
다음은 음의 부호끼리 곱하므로
양의 부호가 되겠죠
즉, + 3sin(5x-3y)dy/dx가 됩니다
즉, + 3sin(5x-3y)dy/dx가 됩니다
 
이제 마지막 항을 양변에 뺍시다
이제 마지막 항을 양변에서 뺍시다
이것은 원래 1dy/dx이고요
여기서 마지막 항을 빼므로
좌변에서는 1dy/dx
빼기 3sin(5x-3y)dy/dx를 합니다
 

Portuguese: 
Então teremos um menos três -
manterei a cor para o três por diversão -
um menos três seno de cinco x 
menos três y dy/dx, do lado esquerdo,
que será igual a
bom, subtraímos isso de ambos os lados,
então no lado direito isso desaparece.
Nos sobra apenas menos cinco seno de
cinco x menos três y.
Estamos na reta final 
para resolver para dy/dx!
Você tem apenas que dividir ambos os lados
da equação por isso,
e obtemos dy/dx igual a isso aqui,
menos cinco vezes seno
de cinco x menos três y.

Georgian: 
გექნებათ -3.
დავტოვებ ამ ფერს, სასაცილოა
3sin(5x-3y) dy/dx's
მარცხენა მხარე
იქნება...
ეს გამოვაკელით ორივე მხარეს, ეს მარჯვენა მხარეს მიდის.
დაგვრჩება -5sin(5x-3y)
რომ ვიპოვოთ dy/dx...
უნდა გაყოთ განტოლების ორივე მხარე ამაზე და და დაგვრჩა
dy/dx უდრის
ამას,
-5sin(5x-3y)

Turkish: 
-
-
Yani sol taraftaki 1 eksi 3 sinüs 5 x eksi 3 y d y d x eşittir...
-
-
Bunu iki taraftan çıkardık, yani sağ tarafta bu gider.
Sadece eksi 5 sinüs 5 x eksi 3 y kalır.
Son düzlükteyiz. d y d x'i bulmak için, denklemin iki tarafını buna bölersiniz ve şu ifadeyi elde edersiniz.
-
d y d x eşittir eksi 5 çarpı sinüs 5 x eksi 3 y, bunun tamamı bölü 1 eksi 3 sinüs 5 x eksi 3 y. Ve cevabı bulduk.
-
-

English: 
So you're going to
have 1 minus 3--
I'll keep the color
for the 3 for fun--
3 sine of 5x minus 3y dy/dx's
on the left-hand side,
is going to be
equal to, well, we
subtracted this from both sides.
So on the right-hand side,
this is going to go away.
So we're just going to be
left with a negative 5 sine
of 5x minus 3y.
And we're in the
home stretch now.
To solve for dy/dx,
we just have to divide
both sides of the
equation by this.
And we are left with dy/dx is
equal to this thing, negative
5 times the sine of 5x minus 3y.

Korean: 
즉, 1 빼기 3
숫자 색을 유지할게요
(1-3sin(5x-3y))dy/dx가 좌변에 남고요,
이것은 우변과 같은데
이 항을 양변에 뺐으니까
우변에서는 이 항이 없어집니다
그러므로 남는 것은
-5sin(5x-3y)입니다
이제 마지막 단계입니다
dy/dx에 대해 정리하기 위해
양변을 이 식으로 나누면 됩니다
그럼 남는 것은 좌변에 dy/dx,
우변에 -5sin(5x-3y)

Czech: 
takže budeme mít
(1 minus 3...
3 nechám jen tak pro
legraci stejnou barvou.
...3 krát sin(5 krát x minus 3 krát y))
krát (dy lomeno dx).
To bude na
levé straně.
Tohle se rovná...
Tohle jsme odečetli od obou stran,
takže na pravé straně to zmizí
a zbude −5 krát
sinus z (5 krát x minus 3 krát y).
Teď už je
skoro hotovo,
protože abychom
osamostatnili dy lomeno dx,
musíme obě strany
rovnice vydělit tímhle.
Zbude nám, že dy lomeno dx
se rovná tomuhle,
tedy −5 krát
sinus z (5 krát x minus 3 krát y),

Tamil: 
dy/dx ஐ இடது பக்கமாக
கொண்டு வந்தால் நமக்கு கிடைப்பது
அடைப்பு 1 கழித்தல் 3 sin
5x கழித்தல் 3y
dy/dx என்பதாகும்.
 
 
இறுதியாக நமக்கு கிடைத்த சமன்பாடு
அடைப்பு 1 கழித்தல் 3 sin
5x கழித்தல் 3y dy/dx சமம் கழித்தல்
5 sin 5x கழித்தல் 3y
dy/dx  வேண்டுமென்பதால் நாம் இருபுரமும்
அடைப்பு 1 கழித்தல் sin அடைப்பு 5x கழித்தல் 3y dy/dx ஆல் வகுக்க வேண்டும்.

Thai: 
คุณจะได้ 1 ลบ 3
ผมจะใช้สามสีเพื่อความสนุกนะ
3 ไซน์ของ 5x ลบ 3y dy/dx
ทางซ้ายมือ
เท่ากับ
ตรงนี้เราลบเจ้านี่ทั้งสองข้าง, งั้นทางขวามือ นี่จะหายไป
เราก็จะเหลือแค่ ลบ 5 ไซน์ของ 5x ลบ 3y
แล้วเราก็ถึงเส้นชัยแล้ว! เวลาแก้หา dy/dx
คุณก็ต้องหารทั้งสองข้างของสมการด้วยเจ้านี่ แล้วเราจะเหลือ
dy/dx เท่ากับ
เจ้านี่, ลบ 5 คูณไซน์
5x ลบ 3y

Bulgarian: 
Ще бъде равно на 1 минус 3...
ще запазя цвета на числото 3, 
за да е забавно.
3 по синус от (5x – 3y) по dy/dx 
от лявата страна.
Лявата страна ще бъде равна на...
Извадихме това от двете страни
 на уравнението.
И така, от дясната страна 
този израз ще изчезне.
Следователно ще остане 
минус 5 по синус от (5x – 3y).
Вече сме в заключителната част.
За да го решим за dy/dx, 
просто трябва да разделим
двете страни на уравнението 
на  този израз.
Отляво ни остава, че dy/dx 
е равно на този израз,
минус 5 по синус от (5x – 3y).

Bulgarian: 
Всичко това е върху 1 минус 
3 по синус  от (5x – 3y).
И ето, че сме готови.

English: 
All of that over 1 minus
3 sine of 5x minus 3y.
And we are done.

Czech: 
to celé lomeno (1 minus
3 krát sinus z (5 krát x minus 3 krát y)).
A máme hotovo.

Portuguese: 
Tudo isso sobre um menos três seno
de cinco x menos três y. E acabamos.
[Legendado por Renata Favalli]
[Revisado por Pilar Dib]

Georgian: 
ეს ყველაფერი შეფარდებული
-3sin(5x-3y) და ჩვენ გავაკეთეთ.

Thai: 
ทั้งหมดนั่นส่วน 1 ลบ 3 ไซน์
ของ 5x ลบ 3y แล้วก็เสร็จแล้ว

Tamil: 
இறுதியில் கிடைப்பது dy/dx சமம் கழித்தல் 5sin அடைப்பு 5x கழித்தல் 3y /
அடைப்பு 1 கழித்தல் 3 sin 5x கழித்தல் 3y

Korean: 
나누기 (1-3sin(5x-3y))가 됩니다
이게 끝입니다

Turkish: 
-
-
