
English: 
Consider the functions f and
g with the graphs shown below.
If capital G of x is equal to g
of f of x whole thing squared,
what is the value of G
prime, capital G prime, of 5?
And I encourage you to
now pause this video
and try to solve it on your own.
So let's try to think
through this somewhat
complicated-looking function
definition right over here.
So we have capital G of x.
And actually, let me
write it this way.
Let me write it this way,
I'll do it in yellow.
We have capital G of x is
equal to this quantity squared.
What we're squaring
is g of f of x.
g of f of x is what
we're squaring.
Or another way to
write G of x, If h of x
were to be equal
to x squared, we

Korean: 
 
아래와 같은 그래프를 가진
f와 g 함수가 있다고 합시다
G(x)=(g(f(x)))²일 때
G'(5)의 값을 구해 봅시다
잠시 영상을 멈추고
직접 풀어보시기 바랍니다
이제 다소 복잡해 보이는
이 함수를 들여다 봅시다
G(x)가 있지요
노란 색으로
써보겠습니다
G(x)는 여기 제곱으로 나타납니다
G(x)=(          )²
제곱 하는것은 g(f(x))입니다
G(x)=(g(f(x)))²
제곱 하는것은 g(f(x))입니다
G(x)=(g(f(x)))²
이렇게도 나타낼 수 있습니다
h(x)=x²이라고 한다면

Portuguese: 
Considere as funções f e g
com os gráficos abaixo.
Se G de x é igual a g
de f de x, tudo ao quadrado,
qual é o valor de
G linha de cinco?
E eu te encorajo
a pausar o vídeo
e tentar resolver
sozinho.
Vamos tentar pensar
sobre esse problema
meio complicado sobre
funções.
Temos G de x.
Na verdade,
vou escrever assim.
Vou escrever em amarelo.
Temos G de x que é igual
a essa quantia ao quadrado.
O que estamos elevando é
g de f de x.
g de f de x. é 
o que estamos elevando.
Um outro jeito de escrever
g de x, se h de x
fosse igual a x ao quadrado,

Thai: 
 
พิจารณาฟังก์ชัน f กับ g วาดเป็นกราฟข้างล่าง
ถ้า G ใหญ่ของ x เท่ากับ g ของ f ของ x 
ทั้งหมดกำลังสอง
ค่าของ G ไพรม์, G ใหญ่ไพรม์ของ 5 
เป็นเท่าใด?
ผมแนะนำให้คุณหยุดวิดีโอตอนนี้
แล้วพยายามหาคำตอบเองก่อน
ลองคิดถึงนิยามฟังก์ชัน
ที่ดูค่อนข้างซับซ้อนตรงนี้กัน
เรามี G ใหญ่ของ x
ที่จริง ขอผมเขียนแบบนี้นะ
ขอผมเขียนแบบนี้ ผมจะใช้สีเหลือง
เรามี G ใหญ่ของ x เท่ากับปริมาณนี้กำลังสอง
สิ่งที่เรายกกำลังสองคือ g ของ f ของ x
g ของ f ของ x คือสิ่งที่เรายกกำลังสอง
หรือวิธีเขียน G ของ x อีกอย่าง ถ้า h ของ x
เท่ากับ x กำลังสอง เรา

Bulgarian: 
 
Дадени са функциите f и g
и съответните им графики.
Ако главно G(х) е равно на g от f(х),
цялото на квадрат,
каква е стойността на главно G' от 5?
Насърчавам те да спреш
видеото на пауза
и да се опиташ да го 
намериш самостоятелно.
Да разгледаме това донякъде
сложно на вид
определение на функцията
ето тук.
Имаме G(х).
Всъщност ще го напиша така,
ще използвам жълто.
Имаме G(х) е равно
на това на квадрат.
Значи повдигаме
на квадрат g от f(х).
Друг начин да запишем
G(х) е – ако h(х)
е равно на х^2,

Portuguese: 
poderíamos escrever G de x 
sendo igual a h disso aqui,
h de g de f de x.
Vou copiar para
poder colar
para eu não ter que
ficar mudando de cor.
Então, copiar e colar, 
e pronto.
É outro jeito de escrever
G de x, onde qualquer
g de f de x,
nós aplicamos a h de x,
que é basicamente elevar a dois.
Há alguns jeitos
para poder escrever
a derivada de G 
com relação a x.
E você pode imaginar
que vai
envolver a regra
da Cadeia.
Mas gosto de escrever
só pra esclarecer,
pra mim mesmo, o que
está acontecendo
e me certificar que
de fato faz sentido.
Uma das coisas que
poderíamos escrever,
poderíamos escrever
a derivada de G
com relação-- vou misturar
notações um pouco--
a derivada
de G de x com relação

Bulgarian: 
тогава G(х) е равно на h от това,
h от g от f(x).
Ще копирам и ще поставя това тук,
за да не се налага 
да сменям цветовете.
Копирам, поставям, готово.
Това е друг начин да запишем
G(х), като независимо
каква е g(f(x)),
когато ги въведем в h(х), ние
просто ги повдигаме на квадрат.
Има няколко начина, по които
можем да запишем
производната на G спрямо х.
Сигурно се досещаш, че ще търсим
производна на сложна функция.
Но искам да го запиша,
за да ми е по-ясно
какво точно се случва
и за да съм сигурен,
че всичко е правилно.
Това, което можем
да напишем,
можем да напишем 
производната на G спрямо...
ще смеся малко начините
на записване...
но ще запиша, че производната
на G(х) спрямо х

Korean: 
G(x)를 이렇게 나타낼 수도 있습니다
G(x)=h(g(f(x)))
설명을 원활히 하기 위해
복사 붙여넣기를 조금만 쓰겠습니다
G(x)=h(g(f(x)))
이렇게 정의할 수도 있는 이유는
h(x)에서 x에 g(f(x))를 대입하면
g(f(x))를 제곱하는 것으로
(g(f(x)))²와 같기 때문입니다
G(x)의 도함수를 구하는 방법도
몇 가지가 있습니다
여러분이 짐작하시는 대로
연쇄 법칙과 관련이 있습니다
하지만 이해하기 쉽도록
다시 풀어서
정리해 보겠습니다
시작해보겠습니다
G(x)를 미분하면
G(x)를 미분하면
G(x)를 x에 대해 미분하면

English: 
could write G of x is equal
to h of this business, h
of g of f of x.
Let me just copy
and paste that so I
don't have to keep
switching colors.
So copy and paste, there we go.
So this is another
way of writing
G of x, where
whatever g of f of x,
we input then to h of x, which
is really just squaring it.
So there's a couple of
ways that we can write out
the derivative of capital
G with respect to x.
And you could
imagine this is going
to involve the chain rule.
But I like to write it
out, just to clarify
in my head what's going
on and to make sure
that it actually
makes some sense.
So one thing that
we could write,
we could write the
derivative of G
with respect-- I'll mix
notations a little bit--
but I'll write the derivative
of G of x with respect

Thai: 
ก็เขียน G ของ x ได้ว่าเท่ากับ h ของทั้งหมดนี้
h ของ g ของ f ของ x
ขอผมลอกและวาง ผม
จะได้ไม่ต้องเปลี่ยนสีเรื่อยๆ
ลอกและวาง ได้แล้ว
นี่คือวิธีเขียน
G ของ x อีกอย่าง โดย g ของ f ของ x
เราใส่มันเข้าไปใน h ของ x ซึ่งก็คือ
การยกกำลังสองมัน
มันมีวิธีเขียน
อนุพันธ์ของ G ใหญ่เทียบกับ x ได้หลายวิธี
และคุณนึกได้ว่า อันนี้จะ
เกี่ยวข้องกับกฎลูกโซ่
แต่ผมชอบเขียนมันออกมา เพื่อให้เห็นชัด
ว่าเกิดอะไรขึ้น และเพื่อให้แน่ใจ
ว่ามันสมเหตุสมผลจริง
สิ่งหนึ่งที่เราเขียนได้
เราเขียนอนุพันธ์ของ G
เทียบกับ -- ผมผสมสัญลักษณ์หน่อย --
ผมจะเขียนว่าอนุพันธ์ของ G ของ x เทียบกับ

English: 
to x is equal to the
derivative of this whole thing.
So let me copy and paste
it, copy and paste.
It's equal to this derivative
of this whole thing with respect
to what's inside of
that whole thing.
So if you wanted to treat
g of f of x as a variable,
so with respect to that.
So copy and paste.
So it's going to be the
derivative of this whole thing
with respect to g of f of
x times the derivative of g
of f of x with respect to f
of x, with respect to-- I'll
just copy and paste this
part, whoops-- with respect
to f of x.
And I like to write this out.
It feels good.

Korean: 
여기 이 괄호 안을 미분한 것과 같습니다
복사해서 붙여 넣겠습니다
결국 h(g(f(x)))를
이 괄호 안의 값에 대해
미분한 것과 같습니다
g(f(x))를 변수로 보고
h를 변수에 대해 미분을 하는 겁니다
다시 복사해서 붙여 넣겠습니다
여기 이 부분을
g(f(x))에 대해 미분한 것에
g(f(x))를 f(x)에 대해 미분한 것을 곱하고
다시 복사해서 붙여 넣습니다 에이구
f(x)에 대해 미분한 것과 같습니다
저는 이렇게 실제로 쓰는 것을
정말 좋아합니다

Thai: 
x เท่ากับอนุพันธ์ของทั้งหมดนี้
ขอผมลอกและวางนะ ลอกและวาง
มันเท่ากับอนุพันธ์ของทั้งหมดนี้เทียบกับ
สิ่งที่อยู่ข้างในทั้งหมดนี้
ถ้าคุณอยากให้ g ของ f ของ x เป็นตัวแปร
เทียบกับค่านั้น
ลอกและวาง
มันจะเท่ากับอนุพันธ์ของทั้งหมดนี้
เทียบกับ g ของ f ของ x คูณอนุพันธ์ของ g
ของ f ของ x เทียบกับ f ของ x เทียบกับ --
ผมจะลอกและวางส่วนนี้ โอ๊ะ -- เทียบ
กับ f ของ x
ผมชอบเขียนมันออกมา
มันรู้สึกดี

Bulgarian: 
е равна на производната
на цялото това нещо.
Ще копирам и ще го поставя.
Равно е на производната
на това цялото нещо спрямо
това, което е тук вътре в скобите.
Ако искаш да разглеждаш
g от f(х) като променлива,
значи спрямо това.
Значи копирам и поставям.
Значи производната на това
цялото нещо
спрямо g от f(х) 
по производната на g от f(х)
спрямо f(х) спрямо...
просто копирам и поставям тази част...
опа... спрямо f(х).
Искам да запиша това.
Изглежда добре.

Portuguese: 
a x é igual à
derivada disso tudo.
Vou copiar e colar isso.

Thai: 
มันดูเหมือนว่า พวกมันเป็นพจน์เศษส่วนของ
ดิฟเฟอเรนเชียล
มันเป็นสัญลักษณ์มากกว่าจะเป็นเช่นนั้นจริงๆ
แต่มันรู้สึกดี อย่างน้อยในความคิดผม
ที่เห็นว่าทำไมมันถึงใช้ได้
ตามสัญชาตญาณมากกว่า
เทียบกับ f ของ x คูณอนุพันธ์ของ -- ผม
จะไม่ใช้สัญลักษณ์มาตรฐานตรงนี้
แต่มันช่วยให้ผมเข้าใจหลักการได้ -- คูณ
อนุพันธ์ของ f ของ x เทียบกับ x
หรือวิธีเขียนอันนี้อีกอย่าง
คือว่า G ไพรม์ของ x เท่ากับ h ไพรม์
ของ g ของ f ของ x, h ไพรม์ของ -- ที่จริง
ขอผมทำตรงนี้ดีกว่า -- h ไพรม์ของอันนี้
 
ลอกและวาง h ไพรม์ของตัวนั้น

Bulgarian: 
Изглежда, че това са рационални
изрази с диференциали.
Това е по-скоро начин на записване,
което да не се приема буквално.
Изглежда добре, или поне
на мен ми се струва
че това е по-логичен начин
защо това работи.
Значи спрямо f(х) по 
производната на...
използвам нестандартен начин
на записване,
но това ще помогне по-добре
да концептуализираме това –
производната на f(х) спрямо х.
Друг начин да запишем това е като
G'(х) е равно на h' от
g от f(х),
h' от... ще го направя тук –
h' от това.
Копирам и поставям,
h' от това,

Korean: 
미분연산들의 곱연산인 것처럼
보이기도 하고
말로 설명하는 것 보다
수학 기호를 쓰는 것이
풀이를 정리하는 데
적어도 제 생각에는
더 직관적인 방법입니다
혹시 제가 표준 표기법을 
따르지 않더라도
여러분의 이해를 돕기 위한 것이라고
이해해 주시기 바랍니다
다시 f(x)를 x에 대해 미분한 것을
곱한 것과 같습니다
이렇게 나타낼 수도 있습니다
G'(x)=h'(g(f(x)))
G'(x)=h'(g(f(x)))
G'(x)=h'(g(f(x)))
G'(x)=h'(g(f(x)))
G'(x)=h'(g(f(x)))

English: 
It looks like these are rational
expressions with differentials.
It's really a notation more
than to be taken literally.
But it feels good, or
at least in my mind
it's a little bit more intuitive
why all of this works out.
So with respect to f of x times
the derivative of-- and I'm
using non-standard
notation here,
but it helps me really
conceptualize this-- times
the derivative of f of
x with respect to x.
Or another way we
could write this
is G prime of x is
equal to h prime
of g of f of x, h
prime of-- actually,
let me do it here--
h prime of this.
So copy and paste,
h prime of that,

Korean: 
곱하기 g'(f(x))
복사해서 붙여넣어 주고요
곱하기 g'(f(x))
괄호를 넣겠습니다
곱하기 f'(x)
 
여러분의 이해를 돕기 위해
상당히 복잡해 보이는
수식을 사용했지만
분수와 마찬가지로
이 부분들은 서로
상쇄시킬 수 있습니다
마지막에 남는 것은
x에 대한 h(g(f(x)))의 도함수입니다
우리가 원래 원했던 값이지요
여기 괄호를 씌워주면
더 정확하겠지요
다르게 표현하면
이 부분은
h'(g(f(x)))로 나타낼 수 있고
이 부분은 g'(f(x))가 되고
여기는 f'(x)가 됩니다
여기까지 이해했다면
이 문제의 답을 구하는 것은
어렵지 않습니다

English: 
times g prime of f of x,
times g prime of this.
So copy and then paste.
So times g prime of that.
Put some parentheses there.
Times f prime of x.
And I like writing it this
way, because you notice
if these were-- and once
again, this is more notation,
but it gives a sense
of what's going on.
If you did view
these as fractions,
that would cancel with that.
That would cancel with that.
You're taking the derivative
of everything with respect
to x, which is exactly
what you wanted to do.
And let me put some
parentheses here
so it makes a little bit
clearer what's going on.
But this thing, in
my brain, I like
to translate that
as, well, that's
just h prime of g of f of x.
This is g prime of f of x.
This is f prime of x.
And going from this
to try to answer
your question, the question
that they're asking us actually
isn't too bad.

Bulgarian: 
по g' от f(х), по g' от това.
Значи копираме и поставяме.
Значи това по g' от това.
Поставям тук скоби.
По f'(х).
Харесва ми да го направя
по този начин, защото ще забележиш,
че ако това беше... и отново,
това е само начин на записване,
но това ни дава представа
какво се случва.
Ако разглеждаме това
като дроби,
тези биха се съкратили.
Това ще се съкрати с това.
Намираме производната на
всичко спрямо х,
което е точно това, което
искахме да направим.
Ще поставя тук скоби,
така става по-ясно какво
се случва.
Но това нещо, според мен,
предпочитам да го изразя като
h' от g от f(х).
Това е g' от f(х).
Това е f'(х).
Изхождайки от това, за да се опитам
да отговоря на въпроса,
въпросът, който ни задават
всъщност не е толкова труден.

Thai: 
คูณ g ไพรม์ของ f ของ x, คูณ g ไพรม์ของอันนี้
ลอกแล้วก็วาง
คูณ g ไพรม์ของตัวนั้น
ใส่วงเล็บตรงนี้
คูณ f ไพรม์ของ x
 
และผมชอบเขียนแบบนี้ เพราะคุณสังเกต
ว่าถ้าพวกนี้ -- ย้ำอีกครั้ง 
นี่เป็นสัญลักษณ์มากกว่า
แต่มันทำให้เราเข้าใจสิ่งที่เกิดขึ้น
ถ้าคุณมองพวกนี้เป็นเศษส่วน
อันนั้นจะตัดกับอันนั้น
อันนั้นจะตัดกับอันนั้น
คุณกำลังหาอนุพันธ์ของทุกอย่างเทียบกับ
x ซึ่งก็คือสิ่งที่คุณอยากทำพอดี
ขอผมใส่วงเล็บตรงนี้
มันจะได้ชัดเจนว่าเกิดอะไรขึ้น
แต่ตัวนี้ ในสมองผม ผมชอบ
แปลมันว่า มัน
คือ h ไพรม์ของ g ของ f ของ x
นี่คือ g ไพรม์ของ f ของ x
นี่คือ f ไพรม์ของ x
และจากอันนี้ เวลาพยายามตอบ
คำถาม คำถามที่เขาถามเรา
ไม่ได้ยากนัก

Thai: 
เราอยากรู้ว่า G ไพรม์ของ 5 เป็นเท่าใด?
ทุกที่ที่เราเห็น x ลองแทนมันด้วย 5
เราจะบอกว่า เราต้องหา G ไพรม์ของ 5
 
G ไพรม์ของ 5 เท่ากับ -- ที่จริง
ขอผมลอกและวางทั้งหมดนี้นะ
ลอกและวาง
ขอผม ทุกที่ที่ผมเห็น x
ผมจะแทนที่มันด้วย 5
ขอผมกำจัดอันนั้นนะ
ขอผมกำจัดอันนั้น
ขอผมกำจัดอันนั้น
แล้วผมมี 5, 5 และ 5
f ของ 5 คืออะไร?
f ของ 5 เท่ากับลบ 1
อันนี้ตรงนี้ลดรูปเหลือลบ 1
อันนี้ตรงนี้ลดรูปเหลือลบ 1
แล้ว f ไพรม์ของลบ 5 เป็นเท่าใด?
นั่นคือความชันของเส้นสัมผัส

Korean: 
G'(5)의 값을 구하려면
x의 자리에 5를 대입하면 됩니다
G'(5)의 값을 구해야 하니까
G'(5)의 값을 구해야 하니까
G'(5)의 값을 구해야 하니까
우선 수식 전체를 복사해서
붙여 넣겠습니다
그리고 모든 x의 자리에
5를 대입합니다
x를 모두 지우고
x를 모두 지우고
x를 모두 지우고
빈 자리에 모두 5를 넣겠습니다
f(5)의 값이 뭘까요?
f(5)=-1입니다
따라서 f(5)는 각각 -1로 대체합니다
따라서 f(5)는 각각 -1로 대체합니다
그러면 f'(5)의 값은 뭘까요?
이 점에서의

English: 
So we want to know,
what's G prime of 5?
So everywhere we see an
x, let's change it to a 5.
So we're going to say, we need
to figure out what G prime of 5
is.
G prime of 5 is equal
to-- and actually,
let me just copy and
paste this whole thing.
So copy and paste.
And so let me, everywhere
where I see an x,
I'm going to
replace it with a 5.
So let me get rid of that.
Let me get rid of that.
And let me get rid of that.
And so I have a 5, a 5, and a 5.
So what is f of 5?
f of 5 is equal to negative 1.
So this right over here
simplifies to negative 1.
This right over here
simplifies to negative 1.
And what's f prime
of negative 5?
Well, that's the slope
of the tangent line

Bulgarian: 
Бихме искали да знаем
колко е G' от 5.
Навсякъде, където виждаме х,
ще го променим на 5.
Значи търсим колко е G' от 5.
G' от 5 е равно на... и всъщност
само ще копирам и поставя
цялото нещо.
Копирам и поставям.
Сега навсякъде, където
виждам х,
ще го заместя с 5.
Ще се отърва от това,
ще се отърва от това.
И ще се отърва и от това.
Значи имам 5, 5 и 5.
Колко е f(5)?
f от 5 е равно на –1.
Това тук се опростява
до –1.
Това тук се опростява
до –1.
Колко е f' от 5?

Thai: 
ที่จุดนี่ตรงนี้
และเราเห็นว่าอนุพันธ์ หรือความชัน
ของเส้นสัมผัสตรงนี้เป็น 0
ค่านี่ตรงนี้จะเท่ากับ 0
ทีนี้ มันน่าสนใจมาก
เราพยายมหา ว่า g ของลบ 1 เป็นเท่าใด?
g ไพรม์ของลบ 1 เป็นเท่าใด?
คุณบอกได้ว่า g ของลบ 1, g ของลบ 1
เราเห็นลบ 1. g ไพรม์ของลบ 1 
คือความชันตรงนี้
ซึ่งก็คือลบ 1 เช่นกัน
แล้วเราก็คำนวณ h ไพรม์ของค่าเหล่านี้
ฯลฯ
แต่เราไม่ต้องทำแล้ว
เพราะนี่คือผลคูณของสามค่า
และหนึ่งในนั้นเท่ากับ 0
0 คูณอะไรก็ตาม คูณอะไรก็ตาม
จะเท่ากับ 0
วิธีคิดอีกอย่างคือว่า f ของ x
ไม่เปลี่ยนไปเมื่อ x เท่ากับ 5
ถ้า f ของ x ไม่เปลี่ยนเมื่อ x เท่ากับ 5
ค่านำเข้าของ g จะไม่เปลี่ยนไป
ฟังก์ชัน g จะไม่เปลี่ยน -- ในการประกอบ
g ของ f ของ x -- จะไม่เปลี่ยน
แล้ว h ของ g ของ f ของ x ก็ไม่เปลี่ยน

Korean: 
접선의 기울기를 보면 됩니다
그런데 이 점에서의
접선의 기울기는 0입니다
그러므로 이 값은 0이 됩니다
아주 흥미롭네요
계속 해 봅시다
g(-1)의 값은 무엇일까요?
g'(-1)의 값은 무엇일까요?
g(-1)의 값은 -1이고
g'(-1)은 이 접선의 기울기이므로
역시 -1이 됩니다
이제 계산만 남았습니다
이제 계산만 남았습니다
아니 굳이 계산할 필요도 없겠습니다
이 세 값을 곱해야 하는데
여기 이 값은 0이기 때문입니다
0에는 어떤 수를 곱해도
0이 되니까요
이렇게 생각해 볼 수도 있습니다
x가 5일 때 f(x)의 값은 
변하지 않습니다
x가 5일 때  f(x) 값에 변화가 없다면
g 함수에 대입하는 값도
변화가 없을 것이고
따라서 g함수의 값도
변화가 없을 것이고
따라서 g(f(x)) 값도
변화가 없을 것이고
h(g(f(x)))의 값도 변하지 않습니다

Bulgarian: 
Това е наклонът на допирателната
в тази точка ето тук.
Виждаме, че производната,
или този наклон
на допирателната тук е 0.
Това тук е равно на 0.
Това е наистина интересно.
Можем да продължим да
опитваме да намерим колко е g от –1.
Колко е g' от –1?
Можем да видим g от –1,
което е –1. g' от –1
е наклонът ето тук,
който също е –1.
После можем да изчислим
h' от тези стойности и т.н.
Но това дори не е нужно, защото
това е произведение от три неща,
като единият множител е нула.
Нула по нещо по нещо друго
винаги е равно на 0.
Друг начин да мислим за това е,
че f(х) не се променя,
когато х е равно на 5.
Ако f(х) не се променя, когато
х е равно на 5,
тогава входният аргумент на g
няма да се промени.
Така че функцията g ще бъде...
в състава на g от f(х)...
това не се променя.
Така че h от g(х) 
няма да се промени.

English: 
at this point right over here.
And we see that the
derivative, or the slope,
of the tangent line here is 0.
So this right over here
is going to be equal to 0.
Now that's really interesting.
So we could keep trying to,
well, what's g of negative 1?
What's g prime of negative 1?
You could see g of
negative 1, g of negative 1
we see is negative 1. g prime
of negative 1 is the slope here,
which is also negative 1.
Then we could calculate
h prime of these values,
et cetera, et cetera.
But we don't even
have to do that.
Because this is the
product of three things,
and one of these things
right over here is a 0.
So 0 times anything
times anything
is going to be equal to 0.
Another way of thinking
about it is, f of x is
isn't changing when
x is equal to 5.
If f of x isn't changing
when x is equal to 5,
then the input into the g
isn't going to be changing.
So the g function isn't going
to be-- in the composition
g of f of x-- isn't
going to be changing.
And so h of g of f of x
isn't going to be changing.

Bulgarian: 
g(х) няма да се промени.
И така производната на G(х)
за х = 5 е равна на 0.

English: 
So g of x isn't
going to be changing.
And so the derivative of
capital G of x at x equals 5
is going to be equal to 0.

Thai: 
G ของ x จึงไม่เปลี่ยนค่า
แล้วอนุพันธ์ของ G ไพรม์ของ x ที่ x เท่ากับ 5
จะเท่ากับ 0

Korean: 
결국 G(x)의 값도 변화가 없으므로
따라서 x가 5일 때 G'(x)의 값은
0이 됩니다
