
Thai: 
สมมุติว่าภาพนี่ตรงนี้คือกราฟของ f เล็กของ x
นั่นคือ f เล็กของ x ตรงนี้
และสมมุติว่าเรามีฟังก์ชัน F ใหญ่ของ x อีกตัว
และถ้าคุณหาอนุพันธ์ของมัน
F ใหญ่ไพรม์ของ x
มันจะเท่ากับ f เล็กของ x, f เล็กของ x
จากข้อมูลนั้น ข้อใดต่อไปนี้ ภาพใดในนี้
เป็นกราฟของ F ใหญ่ของ x ได้?
ผมแนะนำให้คุณหยุดวิดีโอนี้ พยายาม
คิดเองก่อนที่เราจะทำไปด้วยกัน
ถ้า ถ้าเส้นโค้งนี้เป็นอนุพันธ์
ของกราฟหนึ่งในนั้น
นั่นหมายความว่า สำหรับค่า x ใดๆ
มันจะบรรยายอัตราการเปลี่ยนแปลงชั่วขณะ
หรือความชันของเส้นสัมผัส ซึ่ง
ตัวหนึ่งจะเป็น F ใหญ่ที่เป็นไปได้
ลองดูอันนี้กัน

Bulgarian: 
Нека да кажем, че тук е 
графиката на f(х).
Това е f(х) ето тук.
Нека имаме някаква
друга функция F(х).
Ако трябва да намерим нейната
производна F'(х),
тя е равна на f(х).
Като е дадено това, коя
от тези графики
може да съответства на
F(х)?
Насърчавам те да спреш видеото 
и да опиташ самостоятелно,
преди да го направим заедно.
Ако тази крива е
производна на една от тези,
това означава, че за
всяка стойност на х
тя описва моментната
скорост на изменение.
Или какъв е наклонът на
допирателната, за която
една от тези е вероятното F(х).
Да разгледаме няколко неща тук.

English: 
Let's say that this right over here is the
graph of lowercase f of x.
That's lowercase f of x there.
And let's say that we have some other
function capital F of x.
And if you were to take its derivative,
so, capital F prime of x,
that's equal to lowercase f of x, lower
case f of x.
So given that, which of these, which of
these, could
be the graph of capital, of capital F of
x?
And I encourage you to pause this video,
and try and
think about it on your own before we work
through it.
Well if, if this curve is going to be the
derivative of one of them.
That means that any, for any x value
it's describing what the instantaneous
rate of change.
Or what the slope of the tangent line is,
of which
ever one of these is the possible capital
F of x.
So, let's just look at a couple of things
right here

Korean: 
이것을 f(x)의 그래프라 합시다
f(x)입니다
그리고 F(x)라는 
다른 함수가 있다고 합시다
F(x)를 미분하면 
f(x)와 같습니다
F(x)를 미분하면 
f(x)와 같습니다
보기 중에서
무엇이 F(x)의 그래프일까요?
보기 중에서
무엇이 F(x)의 그래프일까요?
동영상을 멈추고 풀이를 하기 전에
푸는 것을 권장합니다
동영상을 멈추고 풀이를 하기 전에
푸는 것을 권장합니다
이 곡선이 저 그래프들 중 
하나를 미분한 것이라면
어떤 x값에 대해
순간적인 변화율을 설명하거나
어떤 x값에 대해
순간적인 변화율을 설명하거나
이 중에 F(x)인 것의
접선의 기울기를 설명합니다
이 중에 F(x)인 것의
접선의 기울기를 설명합니다
몇 가지를 봅시다

Polish: 
Powiedzmy, że to jest wykres małego f od x.
To małe f od x.
Powiedzmy, że mamy inną funkcję wielkie F od x.
Jej pochodna, czyli wielkie F prim od x,
wynosi małe f od x.
Wiedząc to, który z nich
będzie wykresem wielkiego F od x?
Zachęcam do zatrzymania filmu i próby
przemyślenia tego, zanim to rozwiążemy.
Jeśli ta krzywa jest pochodną jednego z nich,
to oznacza, że dla każdej wartości x
opisuje tempo zmian.
Albo jakie jest nachylenie stycznej,
w rozważanych przypadkach na wielkie F od x.
Spójrzmy na kilka szczegółów,

Portuguese: 
Digamos que isso aqui seja o gráfico
de f minúsculo de x.
Esta é a f minúsculo de x.
E suponhamos uma outra função
F maiúsculo de x.
E se você calcular sua derivada,
F linha maiúsculo de x.
Isso é igual a f minúsculo de x.
Sabendo disso, qual desses poderia ser
o gráfico de F maiúsculo de x?
E eu sugiro que você pare o vídeo e pense
nisso antes de trabalharmos juntos.
Bom, se essa curva vai ser a derivada
de uma delas,
isso significa que para todo valor de x
isto esta descrevendo a taxa de variação
instantânea.
Ou a inclinação da reta tangente de
qualquer uma destas possíveis F de x.
Vamos apenas observar algumas coisas aqui.

Thai: 
เรารู้อะไรเกี่ยวกับ f เล็กของ x บ้าง?
เรารู้ไหมว่าอะไรเป็นอนุพันธ์ของตัวหนึ่งในนี้?
สิ่งหนึ่งที่เรารู้คือว่ามันเป็นบวกเสมอ
มัน มันมี เมื่อเราไปที่ลบอนันต์
เส้นกำกับของมันเข้าหา 0
แต่มันเป็นบวกเสมอ
เนื่องจากนี่คือการบรรยาย
ความชันของกราฟหนึ่งในนี้
นั่นหมายความว่าความชันของกราฟหนึ่งในนั้น
จากตัวเลือกของเรา ต้องเป็นบวกเสมอ
และถ้าเราดูอันนี้ ความชัน
ของเส้นสัมผัสตรงนี จะเป็นบวกเสมอจริง
ความชันของเส้นสัมผัสตรงนี้
ดูเหมือนว่าเป็นบวก
ทุกครั้งที่เราเพิ่ม x ค่า y จะเพิ่มขึ้น
ตรงนี้มันเป็นบวก
แต่ตรงนี้มันเป็นลบ
เมื่อเราเพิ่ม x เราลดค่า x
เราจึงตัด เราจึงตัดอันนี้ได้
แล้ว เรารู้อะไรอีก?
นี่คืออนุพันธ์
อันนี้บอกเราว่าความชันของเส้นสัมผัส
ตัวอย่างเช่น เมื่อ x เท่ากับ เมื่อ x เท่ากับลบ 4
f ของ, f ของลบ 4 ใกล้กับ 0 ทีเดียว

Portuguese: 
O que sabemos sobre a f de x,
que é a derivada de um desses aqui?
Sabemos que ela é sempre positiva.
Tem sua assíntota passando por zero
à medida que vamos para infinito negativo.
Mas é sempre positiva.
Uma vez que isso está descrevendo
a inclinação de uma dessas,
isso significa que a inclinação
de uma dessas candidatas
deve ser sempre positiva.
Se olharmos pra cá, a inclinação da reta
tangente é, de fato, sempre positiva.
Aqui também parece que é sempre positiva.
Sempre que aumentamos x,
y também aumenta.
Aqui é positiva.
Mas aqui é negativa.
Quando x aumenta, y diminui.
Podemos descartá-lo.
O que mais nós sabemos?
Bom, isso é a derivada.
Nos diz a inclinação da reta tangente.
Por exemplo, quando x é menos quatro
f de menos quatro é bem perto de zero.

English: 
so what, what do we know about lower case
f of x?
What do we know of which is the derivative
of one of these?
Well, one thing we know is it's always
positive.
It, it has as we go to negative infinity,
it asymptotes towards 0.
But it's always positive.
So since this is describing the slope of
one of these.
That means that the slope of one of these
always,
or out of the candidates, has to always be
positive.
And, if we look at this, the slope
of the tangent line here is, indeed,
always positive.
The slope of the tangent line here does
look like it's positive.
Every time we increase an x, we're
increasing by y.
Here it's positive.
But here it's negative.
When we increase by x, we decrease by y.
So, we can rule, we can rule this one out.
Now, what else, what else do we know?
Well, this is the derivative.
This is telling us the slope of the
tangent line.
So, for example, when x is equal to, when
x is equal to negative 4,
f of, f of negative 4 is pretty close to
0.

Bulgarian: 
Какво знаем за f(х)?
Какво знаем за производните
на всяка от тези?
Едно нещо, което знаем, е
че са винаги положителни.
Когато клони към минус безкрайност,
асимптотата клони към нула.
Но е винаги положителна.
Когато описва наклона
на една от тези,
това означава, че наклонът
на една от тези функции
винаги трябва да е 
положителен.
И ако погледнем това,
наклонът
на допирателната тук,
разбира се, е винаги положителен.
Наклонът на допирателната
права тук е положителен.
Всеки път, когато х нараства,
нараства и у.
Тук е положителен.
Но тук е отрицателен.
Когато х нараства,
у намалява.
Значи можем да изключим тази.
Какво друго знаем?
Това е производната.
Това ни казва наклонът
на допирателната.
Например, когато х = –4,
f(–4) е много близко до 0.

Polish: 
co wiemy o małym f od x?
Wiemy, że jest pochodną jednego z nich.
Wiemy, że jest zawsze dodatnia.
Jeśli przejdziemy z x do minus nieskończoności, zbliża się asymptotycznie do 0.
Ale jest zawsze dodatnia.
Jeżeli to określa nachylenie jednego z nich,
To oznacza, że nachylenie jednego z nich,
jednego z kandydatów jest zawsze dodatnie.
Jeśli spojrzymy na ten, nachylenie
stycznej jest rzeczywiście zawsze dodatnie.
Nachylenie stycznej tutaj wygląda na dodatnie.
Za każdym razem, kiedy zwiększamy x, zwiększamy y.
Tutaj jest dodatnie.
Ale tutaj ujemne.
Kiedy zwiększamy x, zmniejszamy y.
Więc ten możemy odrzucić.
Co jeszcze wiemy?
To jest pochodna.
która mówi nam o nachyleniu stycznej.
Na przykład, kiedy x jest równy minus 4,
f od minus 4 jest bliskie 0.

Korean: 
f(x)에 대해서
무엇을 알고 있을까요?
이들 중 하나를 미분한 함수에 
대해 무엇을 알고 있을까요?
한 가지 아는 것은 
항상 양수라는 점입니다
음의 무한대로 가면 
점근선이 0이 됩니다
하지만 항상 양수입니다
이들 중 하나의 기울기를 
나타내고 있으므로
후보군의 기울기는 
항상 양수가 되어야 합니다
후보군의 기울기는 
항상 양수가 되어야 합니다
이 그래프의 경우 
접선의 기울기를 보면 항상 양수입니다
이 그래프의 경우 
접선의 기울기를 보면 항상 양수입니다
이 그래프의 접선의 기울기는
양수처럼 보입니다
항상 x가 증가하면 y도 증가합니다
여기는 기울기가 양수이지만
여기는 기울기가 음수입니다
x가 증가한다면 y가 감소합니다
조건을 충족하지 않으므로 
이것을 제외할 수 있습니다
또 무엇을 알고 있을까요?
이것은 미분값입니다
접선의 기울기를 나타내고 있습니다
예를 들어 x가 -4라면
f(-4)는 0에 가깝습니다
예를 들어 x가 -4라면
f(-4)는 0에 가깝습니다

Polish: 
Jest bliskie 0.
Więc to wynosi nieco więcej niż 0.
To nam mówi o tym, że nachylenie stycznej do wielkiego F od x
jest bliskie 0, dla x równego minus 4.
Zobaczmy, kiedy x wynosi minus 4, nachylenie stycznej
tutaj, nie jest bliskie 0, wygląda na bliższe 1.
Możemy to odrzucić.
Tutaj, kiedy x wynosi minus 4, nachylenie stycznej
jest bliskie 0.
Więc tego nie odrzucamy.
Tutaj nachylenie stycznej, kiedy
x jest równy minus 4, także wygląda na bliskie 0.
Więc tych dwóch nie odrzucamy.
Spójrzmy na to inaczej.
Wybierzmy inny punkt.
Kiedy x jest równy 0, f od 0 wygląda na bliskie 1.
Nie wiemy, czy to dokładnie 1.
Wygląda na to, że prawie.
Prawie równe 1.

English: 
It's pretty close to 0.
So, it's slightly, slightly more than 0.
So, that tells us that the slope of
tangent line of capital F
of x has to be pretty close to 0, when x
equals negative 4.
So, let's see, when x equals negative 4,
the slope of tangent
line, here, isn't close to 0, this
actually looks closer to 1.
So, we could rule this one out.
Over here, when x is equal to negative 4,
the slope of
the tangent line, yeah, that actually does
look pretty close to 0.
So I won't rule that one out.
And over here, the slope of the tangent
line, when x
is equal to negative 4, that also looks
pretty close to 0.
So these are still both in the running.
So let's see how we can think of it
different.
So let's just pick another point.
When x is equal to, when x is equal to 0,
f of 0 looks like it's pretty close to 1.
I don't know if it's exactly to 1.
Actually it looks almost exactly.
Almost exactly equal to 1.

Thai: 
มันใกล้กับ 0
มันมากกว่า 0 เล็กน้อย
มันจึงบอกเราว่าความชันของเส้นสัมผัส
ของ F ใหญ่
ของ x ต้องใกล้กับ 0 มาก เมื่อ x เท่ากับลบ 4
ลองดู เมื่อ x เท่ากับลบ 4 
ความชันของเส้นสัมผัส
ตรงนี้ มันไม่ใกล้กับ 0 อันนี้ใกล้กับ 1 มากกว่า
เราจึงตัดอันนี้ออกได้
ตรงนี้ เมื่อ x เท่ากับลบ 4 ความชันของ
เส้นสัมผัส ใช่ มันดูใกล้ 0
ผมจึงไม่ตัดอันนี้ออก
แล้วตรงนี้ ความชันของเส้นสัมผัส เมื่อ x
เท่ากับลบ 4 มันดูใกล้ 0 มาก
พวกนี้จึงยังใช้ได้อยู่
ลองดูว่าเราจะแยกมันอย่างไร
ลองเลือกอีกจุดหนึ่ง
เมื่อ x เท่ากับ เมื่อ x เท่ากับ 0
f ของ 0 ดูเหมือนว่า มันใกล้กับ 1 ทีเดียว
ผมไม่รู้ว่ามันเท่ากับ 1 พอดีไหม
มันดูเหมือนจะใช่
มันเกือบเท่ากับ 1

Portuguese: 
Quase zero.
É levemente maior que zero.
Isso nos diz que a inclinação
da reta tangente à F de x
deve ser bem perto de zero,
quando x for igual a menos quatro.
Vejamos, quando x é igual a menos quatro,
a inclinação da reta tangente aqui
não está próxima de zero. Na verdade,
parece mais próxima de um.
Podemos então descartá-lo.
Aqui, quando x é menos quatro,
a inclinação da reta tangente
parece, de fato, bem próxima de zero.
Não vamos descartá-lo.
Aqui, a inclinação da reta tangente,
quando x é igual a menos quatro
também parece bem próxima de zero.
Então esses dois ainda estão na disputa.
Vejamos como podemos pensar nisso
de outra forma.
Vamos escolher outro ponto.
Quando x é igual a zero, f de zero
parece bem próxima de um.
Não sei se é exatamente um.
Mas realmente parece ser.
Quase igual a um.

Bulgarian: 
Много близко до 0.
То е само малко
повече от 0.
Това ни казва, че наклонът
на допирателната на F(х)
трябва да е много близо до 0,
когато х = –4.
Да видим, когато  х = –4, 
наклонът на допирателната
тук е близо до 0, всъщност
това изглежда близо до 1.
Можем да изключим това.
Тук, когато х е равно на –4,
наклонът
на допирателната изглежда
много близо до 0.
Няма да изключваме това.
Тук наклонът на допирателната,
когато х = –4,
също изглежда много близък до 0.
Значи тези още
са в играта.
Да видим друг начин
на разсъждение.
Да изберем друга точка.
Когато х е равно на 0,
f(0) изглежда доста близко до 1.
Не знам дали е точно 1.
Но изглежда почти точно 1.

Korean: 
예를 들어 x가 -4라면
f(-4)는 0에 가깝습니다
매우 근소하게 0보다 큽니다
x가 -4일때 F(x)의 접선의 
기울기가 0에 가깝다는 것을 뜻합니다
x가 -4일때 F(x)의 접선의 
기울기가 0에 가깝다는 것을 뜻합니다
이 그래프는 x가 -4일때 접선의 
기울기가 0이 아니라 1에 가깝습니다
이 그래프는 x가 -4일때 접선의 
기울기가 0이 아니라 1에 가깝습니다
조건을 충족하지 않으므로 
이것을 제외할 수 있습니다
이 그래프는 x가 -4라면
접선의 기울기가 0에 가까워집니다
이 그래프는 x가 -4라면
접선의 기울기가 0에 가까워집니다
그러므로 제외하지 않습니다
이 그래프에서는 x가 -4라면 
접선의 기울기는 0에 가까워집니다
이 그래프에서는 x가 -4라면 
접선의 기울기는 0에 가까워집니다
둘 다 아직 가능한 후보입니다
다른 관점에서 봅시다
다른 점을 골라 봅시다
x가 0이라면 f(0)은 거의 1입니다
정확하게 1이라면 모릅니다
거의 정확하게 1로 보입니다
거의 정확하게 1로 보입니다

Polish: 
Dla wielkiego F od 0
nachylenie stycznej musi być bliskie 1.
Tutaj nachylenie stycznej,
kiedy x jest równe 0, wygląda na mniej niż 1.
To nachylenie na pewno nie jest równe 1.
Tutaj, kiedy x jest równe 0,
nachylenie stycznej
wygląda na bliskie 1.
Więc ten tutaj wygląda
na najlepszego kandydata na wielkie F od x.
Więc to tutaj,
to jest wielkie F od x.
Możecie powiedzieć, że te dwa tutaj wyglądają podobnie.
I rzeczywiście wyglądają prawie identycznie, nawet są identyczne.
Możecie sobie przypomnieć, co wiecie
o różniczkowaniu, ten wygląda jak podstawowa funkcja wykładnicza.

Bulgarian: 
Когато... за F(0)
наклонът на допирателна
трябва да е близо до 1.
Тук горе наклонът на 
допирателната, когато
х = 0 изглежда, че
е по-малък от 1.
Определено наклонът не е 1.
Ето тук, когато х = 0,
наклонът на допирателната изглежда
че е много, много близо до 1.
Значи това тук изглежда
най-добрият кандидат за F(х).
Ето това тук.
Това е F(х).
Може да кажеш, че тези
си приличат.
Наистина те изглеждат
почти идентични.
Може би си спомняш от това, което
знаеш за диференцирането,
че това изглежда като основна
показателна функция.

Korean: 
F(0)일때 
접선의 기울기가 1에 가까워야 합니다
F(0)일때 
접선의 기울기가 1에 가까워야 합니다
이 그래프는 x가 0일때 
접선의 기울기가 1보다 작습니다
이 그래프는 x가 0일때 
접선의 기울기가 1보다 작습니다
기울기가 확실히 1이 아닙니다
반면 이 그래프는 x가 0일때
접선의 기울기가 1에 가깝습니다
반면 이 그래프는 x가 0일때
접선의 기울기가 1에 가깝습니다
반면 이 그래프는 x가 0일때
접선의 기울기가 1에 가깝습니다
조건에 충족하는 
F(x)의 그래프입니다
조건에 충족하는 
F(x)의 그래프입니다
따라서 이것이 F(x)입니다
따라서 이것이 F(x)입니다
이 두 그래프가 
매우 비슷하게 보일 수도 있습니다
사실상 거의 똑같게 생겼습니다
미분에 대해 기억한다면 이것들은
지수함수의 그래프들처럼 생겼습니다
미분에 대해 기억한다면 이것들은
지수함수의 그래프들처럼 생겼습니다

Thai: 
เมื่อ F ใหญ่ของ F ใหญ่ของ 0
ความชันของเส้นสัมผัสต้องใกล้กับ 1
ตรงนี้ ความชันของเส้นสัมผัส
เมื่อ x เท่ากับ 0 มันดูน้อยกว่า 1
ความชันนี้ไม่ใช่ 1 แน่นอน
ในขณะที่ตรงนี้ เมื่อ x เท่ากับ 0
ความชันของเส้นสัมผัสดูเหมือน
ความชันของเส้น
สัมผัสดูใกล้กับ 1 มากๆ
กราฟนี่ ตรงนี้ ดูเหมือน
จะเป็นตัวเลือกที่ดีที่สุดสำหรับ F ใหญ่ของ x
กราฟนั่นตรงนั้น
ขอผม นั่นคือ F ใหญ่ของ x
และคุณอาจบอกว่า เฮ้ สองตัวนี้ดูเหมือนกันเลย
และที่จริง มันดูเกือบเหมือน 
หรือเหมือนกันพอดี
และคุณอาจจำได้จากที่คุณเรียนเกี่ยวกับ
การหาอนุพันธ์ ฟังก์ชันแบบนี้เหมือน
ฟังก์ชันเอกซ์โพเนนเชียลพื้นฐาน

Portuguese: 
Então, em F de zero
a inclinação da reta tangente
precisa ser bem próxima de um.
Aqui, a inclinação da reta tangente
quando x é igual a zero
parece menor que um.
Essa inclinação com certeza não é um.
Enquanto que aqui, quando x é igual a zero
a inclinação da reta tangente
parece estar bem perto de um.
Então este aqui parece ser o melhor
candidato a F de x.
Portanto esta aqui é a F de x.
E você pode dizer:
Esses dois são bem parecidos.
De fato, eles parecem ser idênticos.
E você pode se lembrar do que você sabia
sobre derivação
que eles parecem na verdade com
a função exponencial básica.

English: 
So when capital F of, so at capital F of
0, the
slope of the tangent line needs to be
pretty close to 1.
So over here the slope of the tangent
line, when
x is equal to 0, that looks smaller than
1.
So this slope is definitely not 1.
While over here, when x is equal to 0.
The slope of the tangent line does look,
the slope of the tangent
line does look pretty, pretty close,
pretty close to 1.
So this, right over here, looks like the
best candidate for capital, for capital F
of x.
So that one right over there.
Lemme, that is capital F of x.
And you might say hey these look similar
to each other.
And fact they look almost or actually they
do look almost identical.
And you might remember from what you knew
about
differentiation, that these actually look
like the basic exponential function.

Portuguese: 
Eu não te pedi pra encontrar
qual era função,
apenas qual seria a possível anti-derivada
desta função.
Esta é a derivada...f minúscula
é a derivada de F maiúscula,
ou você pode dizer que F maiúscula
é a anti-derivada de f minúscula.
Quando você verifica isso,
ambas as funções
são "e" elevado a x.
Porque a derivada de "e" elevado a x
é "e" elevado a x.
[legendado por: Vtor Tocci]
[Revisado por: Victória Celeri]

Korean: 
실제 함수가 무엇인지 
찾으라고 한 것이 아니라
이 함수의 
역도함수를 찾으라고 했었지만
f(x)는 F(x)의 도함수입니다
F(x)가 f(x)의 역도함수라고 
할 수도 있습니다
이 그래프를 자세히 보면 두 함수 
모두가 e^x임을 알 수 있습니다
이 그래프를 자세히보면 
두 함수 모두가 e^x임을 알 수 있습니다
왜냐하면 e^x을 미분하면
e^x 이기 때문입니다

Bulgarian: 
Ако трябва да намериш
действителната функция,
която е вероятната примитивна
функция на тази функция,
това е производната – f(х)
е производна на F(х).
Можем да кажем, че F(х) е
примитивната функция на f(х).
И ако провериш, то
изглежда, че
и двете функции са e^х.
Защото производната на е^х
е равна на е^х.

Thai: 
ผมไม่ได้บอกให้คุณหาว่า
ฟังก์ชันที่เป็นปฏิยานุพันธ์ของฟังก์ชันนี้
จริงๆ แล้วคืออะไร
นี่คืออนุพันธ์ f เล็กคือ อนุพันธ์ของ F ใหญ่
หรือคุณบอกได้ว่า F ใหญ๋เป็น
ปฏิยานุพันธ์ของ f เล็ก
และเมื่อคุณตรวจดู มันดูเหมือนว่า
ฟังก์ชัน ทั้งสองฟังก์ชันนี้ คือ e กำลัง x
เพราะอนุพันธ์ของ e กำลัง x คือ e กำลัง x

Polish: 
Nie prosiłem Was o wyznaczenie funkcji,
dla której szukamy funkcji pierwotnej.
To jest pochodna, małe f jest pochodną wielkiego F,
wielkie F jest funkcją pierwotną małego f.
Kiedy się temu przyjrzymy, zobaczymy, że
obie funkcje to e do x.
Bo pochodną e do x jest e do x.

English: 
Were, were I didn't ask you to find out
what the
actual function was just the possible
anti-derivative of this function would be.
This is the derivative, lower case f is
the, is the derivative of capital
f, or you could say that capital f is an
anti derivative of lower case f.
And when you just inspect this, this looks
like this, the,
the function, both of these functions is,
are e to the x.
Because the derivative of e to the x is e
to the x.
