00:01
In this question.
00:02
It has been asked to explain when and how to use the derivative rules.
00:08
So the first rule is the product rule which says that if y equal to u v then why does equals two u dot v plus u v does.
00:19
Where does represent the first derivative? so let's see when do we need to use the product rule with the help of for example.
00:29
So i'm considering one example here.
00:31
Let's save.
00:33
Let why is equals to x times find it.
00:38
So clearly here we can see that we are having to functions multiplied here.
00:44
X.
00:44
And cynics.
00:45
So i will assume you to be equal to x and we to be equal to sine x.
00:54
Now, i know the product rule.
00:56
So let's say this is our equation one.
01:01
So hands from equation one, what we will get why does equal 2? you does v plus uv does since us act.
01:15
So your last will be just one.
01:18
We as it is that the cynics plus you x vidas we is cynics.
01:26
Sevilla's becomes our cossacks.
01:29
And that is what is my white asked.
01:33
So here if we have to function getting multiplied together, then we use the product rule.
01:39
And this is how we apply the product rule.
01:42
Let's see the 2nd rule, which is the quotient rule.
01:46
So when we have why in the form you are divided by the then white as is given by the u.
01:53
S minus.
01:54
You would as divided by the square.
01:57
Let's consider one example.
02:00
To understand this for example, let why is equals to sign x divided by x square clearly here you can see it is in the form of you baby.
02:16
So i can consider u equal to sine x.
02:22
And we equal to x squared.
02:26
Let's say this is our equation one.
02:29
So from equation one what i can write my widest to be equal to we us minus.
02:40
You'll be less divided by the square...
5 comments
John R.
March 11, 2023
thanks for taking the time to explain the chain rule nimat you made it seem way less complicated for real
Maria H.
June 7, 2023
The transcription of Mr Ps video is hard to understand due to the lack of punctuation and unclear phrasing
Tiffany P.
August 3, 2023
the explanation of the product rule is comprehensive and helpful.
Maria R.
September 21, 2023
thank you for the comprehensive breakdown of the derivative rules and how to apply them! your clear examples made it crystal clear when to use the product rule quotient rule and chain rule you're a rockstar!
Brenda R.
November 26, 2023
thanks for breaking down the derivative rules and providing clear examples! your explanation helped me understand how to use the product rule, quotient rule and chain rule in different scenarios much appreciated