AstroGuy
#Calc. 1 Chain Rule
oak jewelBOT
gloomy rock
It’s a mix of product rule and chain rule
If you can solve that then you can succeed in your exam
sour junco
Isn't that just lovely
gloomy rock
In the derivative part
sour junco
Ok one second
gloomy rock
Remember the steps
gloomy rock
I can't put the fractions together
That’s the thing
gloomy rock
Just give me result as it is
gloomy rock
No
sour junco
😩
gloomy rock
Let me go back:
$f(x)=xln(3x^2^+4)=uv$
u=x v=ln(3x^2+4)
So:
$f’(t)=u’v+uv’$
oak jewelBOT
AstroGuy
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sour junco
yes
sour junco
1
gloomy rock
Alright now v’ requires chain rule which you may have a made a slight error when using it
v=ln(3x^2+4) right?
I stated that initially
What is f(x) and what is g(x)
sour junco
x
gloomy rock
?
sour junco
and ln(3x^2 + 4)
gloomy rock
and ln(3x^2 + 4)
That’s v
sour junco
🥸
gloomy rock
No
gloomy rock
u=x v=ln(3x^2*4) alright?
sour junco
yes
gloomy rock
Because of the product rule
gloomy rock
We have to apply
sour junco
yes we do
gloomy rock
Okay now you said u’=1
sour junco
correct
gloomy rock
Now v’ requires chain rule to be determined.
v=ln(3x^2+1)=f(g(x))
sour junco
xoh
gloomy rock
What is f(x) and g(x)
sour junco
Okay
gloomy rock
Alright. Now plug g(x) in f’(x)
sour junco
1/ 3x^2+4
sour junco
right....... 😀
gloomy rock
v’=6x/(3x^2+4)
u=x
v=ln(3x^2+4)
u’=1
Derivative of the main function is:
u’v+uv’
sour junco
correct
gloomy rock
Well now apply
oak jewelBOT
Eve 🌷
sour junco
it can be a fraction too
sour junco
I am impressed
LOL i try
gloomy rock
You forgot something
sour junco
$f(x) = ln(3x^2+4) + x * 6x/3x^2+4$
oak jewelBOT
Eve 🌷
gloomy rock
6x*x=6x^2
oak jewelBOT
Eve 🌷
gloomy rock
Let me write with parentheses
oak jewelBOT
Eve 🌷
gloomy rock
$ln(3x^2+4)+\frac{6x^2}{3x^2+4}$
oak jewelBOT
AstroGuy
sour junco
Ok show off
gloomy rock
Alright it’s finished
sour junco
How
Literally
if u can do it
to the second one
why not the first one
it can be a fraction too
gloomy rock
Oh you mean putting everything on the same denominator
sour junco
NOOOOOOO
No
two seperate fractions
although
not a bad idea yeah u can make it one fraction too
sour junco
gloomy rock
There will be squared terms everywhere
sour junco
Ok ill just leave it like that
gloomy rock
Ok ill just leave it like that
Yeah
Nothing more to do
But you seem to sometime get confused
Always start by writing u and v
gloomy rock
95% of the time im confused
Actually you managed to do a lot it’s just minor mistakes
sour junco
Always start by writing u and v
Well i also need to learn how to differentiate
the terms
gloomy rock
Well i also need to learn how to differentiate
Once you get u and v, yeah you calculate u’ and v’
sour junco
Yes
gloomy rock
Then: u’v+uv’
And you got the derivative
Sometimes you don’t need product rule
Because it’s one singular function
Just chain rule
sour junco
well thats just power rule yeah
gloomy rock
ln(x^2-2)
No product rule needed
But chain rule needed
You recognize f(g(x)) type of function
It’s called « a composite function »
x*ln(4x^2-3)
sour junco
Ok i need to learn how to recognize that as well
gloomy rock
Product rule + chain rule
sour junco
x*ln(4x^2-3)
this would be product
yes
so
OH
OK
SOOO if its basically like
Only two different types of derivatives
then its chain
if its more
like within each other
product is included
sour junco
Yeah within you mean next to each other?
uhhhh no
like
how we had
ok well actually yes nevermind i guess u do multiply it as well
gloomy rock
If your function can be split into two functions: product rule
sour junco
yes yes
gloomy rock
If you notice that one of these two function is a composite function then chain rule as well
sour junco
Ok now it makes sense
gloomy rock
Ok now it makes sense
Yayyy
sour junco
ANYWAY im sure its late for you and my brain is actually fried so at this point im just going to accept defeat for this exam
gloomy rock
ANYWAY im sure its late for you and my brain is actually fried so at this point ...
When is your exam?
gloomy rock
How many time left before exam
gloomy rock
The thing is… i won’t be at peace if you don’t solve a derivative on your own
sour junco
am
sour junco
The thing is… i won’t be at peace if you don’t solve a derivative on your own
I know but u said u live in france right?
gloomy rock
I know but u said u live in france right?
Yeah but it’s okay
sour junco
No it's not okay
gloomy rock
Just solve one without my intervention
sour junco
Get rest LOL I feel bad
gloomy rock
And I’ll go rest
sour junco
Just solve one without my intervention
UGHHHH I CANNTTTTTTTTT iT'S GONNGA TAKE ANOTHER 40 MINUTES
gloomy rock
UGHHHH I CANNTTTTTTTTT iT'S GONNGA TAKE ANOTHER 40 MINUTES
But you know the way now, don’t you?
sour junco
I'm at a point where i'll throw up if i look at another derivative
gloomy rock
We’ve made many examples
gloomy rock
I'm at a point where i'll throw up if i look at another derivative
Please one last
sour junco
But you know the way now, don’t you?
More than i did going into this for sure
I will have to nap soon then wake up at 1 am to cram hahahah
sour junco
Please one last
Ok give it to me
gloomy rock
Alright let’s say i give you one last function to derivate and if you succeed I’ll go off
gloomy rock
Ok give it to me
Yayyyy
sour junco
Alright let’s say i give you one last function to derivate and if you succeed I’...
I will not succeed
But we can try
😁
gloomy rock
$L(x)=3xln(2x^2+2x)$
silver girder
Hello there
oak jewelBOT
AstroGuy
gloomy rock
Hello there
Hiiiii
sour junco
Ok, let's see
gloomy rock
Ok, let's see
I named it L(x) so you don’t confuse it with f(x) which is for the part for chain rule remember
sour junco
I named it L(x) so you don’t confuse it with f(x) which is for the part for chai...
Oh Lord
gloomy rock
Hello there
How are you??
silver girder
Hmmm
sour junco
No.
gloomy rock
You are solving it right now ?
sour junco
Yes
gloomy rock
Well tell me once you finish
sour junco
wanna see
gloomy rock
Im sure you can do it
sour junco
what i got so far
gloomy rock
Yeah
sour junco
🥲
gloomy rock
Show me
sour junco
Ok
silver girder
What was the function
gloomy rock
But it’s the right answer
silver girder
Seems right
sour junco
what do i do with the 3x?
gloomy rock
You did it!
sour junco
You did it!
gloomy rock
You multiply it by (4x+2)
sour junco
You multiply it by (4x+2)
Oh
Ughhhh can i just leave it like that for now
You know i know
silver girder
Astro is the best baguette
sour junco
Awwww your giving me too much credit..
Not enough 💀
sour junco
Astro is the best baguette
He is
gloomy rock
And you’re welcome
sour junco
Smartest cookie in the bunch
gloomy rock
Astro is the best baguette
AHAHAHAAH
The thing is.. it’s true that we eat a lot of baguette in France
Not even a stereotype
Because it’s a fact
gloomy rock
Ouiii
Alright i think I’ll log off now
Take care of you guys
And Eve, good luck for tomorrow
gloomy rock
Im sorry that i can’t help you any further
gloomy rock
If they don’t ask you to use chain rule directly then don’t use it. Just use shortcuts like (ln(u))=u’/u
Or (e^u)’=u’e^u
gloomy rock
I'm content
Awww moi aussi
sour junco
Yeah oui oui whatever that means
gloomy rock
Ok I will try to memorize
But chain rule will always give you the right answer
gloomy rock
Yeah oui oui whatever that means
😂
gloomy rock
Chain rule can suck a fart
Lollll
gloomy rock
Get your well deserved rest
Thank you Eve
See you Eve! Take care of you
I hope for the best
sour junco
Likewise ☺️
gloomy rock
See you tomorrow
I’ll see if i can review some things with you before the exam
See youuuu
sour junco
I’ll see if i can review some things with you before the exam
I didn’t see this but YES THAT WOULD BE GREATTT. I’ll try to pull an all nighter and if you’re up , I’m bothering you. Sorry!
silver girder
You need to sleep