00:01
All right.
00:02
Here in the black, we've got the next thing we're going to differentiate.
00:05
Okay, w squared plus 3w, all multiplied to w to the negative 1st minus w to the negative 4th.
00:13
Okay.
00:14
So, first things first, we've got two chunks being multiplied together, right? we've got this thing being multiplied to this thing.
00:28
Okay, so that makes us think we should probably use product rule.
00:32
And product rule is in the green there.
00:34
So we'll be following along with that.
00:36
Okay, the first thing we're multiplying is f.
00:40
Okay.
00:41
So f is what i've underlined there, w squared plus 3w.
00:48
G will be the other thing we're multiplying, w to the negative first, minus w to the negative fourth.
00:57
And if we look in the green there, the product rule, we're going to need the derivative of f prime.
01:03
Okay, and we're going to need the derivative of g.
01:04
G -prem.
01:06
All right, so let's look at f prime first.
01:09
We're just going to use power rule on each of the terms.
01:11
W squared, we bring the two down as the coefficient into the coefficient to w, and we lower the power by one.
01:20
So two w to the first.
01:21
Okay, so we can just leave that.
01:23
And then here, well, there's an invisible one right there.
01:27
We'll bring that down into the coefficient, so three times one is still three.
01:31
And then w to the zero, well, that's just one.
01:34
Okay, so three times one is still just three.
01:36
So we get that as our derivative there.
01:39
Okay.
01:40
Moving on to g prime, all right, the derivative of w to the negative first.
01:45
We'll bring the negative one down, so negative one, but i'm not going to write it because we don't really need that.
01:52
It's invisible still there.
01:54
All right.
01:55
W, and now we lower the power by 1, so to the negative 2.
01:59
Make sure you actually lower it.
02:01
Okay.
02:02
Negative 1 minus 1 is negative 2.
02:05
And now we've got minus, okay, and we're going to bring the power at negative 4 down.
02:12
So minus negative 4, w, okay, and then to the, well, negative 5th now.
02:20
We're lowering it by one more, okay.
02:23
I've got minus negative.
02:25
We'll change that to plus, okay, addition, plus 4w to the negative.
02:33
Okay, so i've got all the pieces now.
02:38
We just need to use our product rule here, okay, to take the derivative.
02:43
So we start with f prime.
02:46
So we start with 2w plus 3.
02:50
All right, next thing is g.
02:53
So we multiply that with w to the negative first minus w to the negative fourth.
02:59
Leaving all this in parentheses because they're being multiplied together.
03:02
Okay, next step is plus.
03:07
Okay, i'm doing terrible with all that.
03:11
Okay.
03:12
Okay, next is f.
03:16
All right, so w squared plus 3w.
03:22
And last is multiply that with g prime.
03:25
So negative w to the negative second plus 4w to the negative fifth.
03:32
Okay, so this is our derivative here.
03:35
All right, right here.
03:38
But it's not clean.
03:40
So we're going to try to clean this up.
03:42
All right, so first let's distribute.
03:45
Thanks.
03:46
2w times w negative 1st.
03:49
All right.
03:50
That is going to be 2.
03:53
All right.
03:54
Well, w to the first times w to the negative first...