00:01
My thought process with this problem is to do the product rule.
00:06
X minus 6 is cubed.
00:09
And so what do i mean by the product rule is here's the product.
00:13
You gotta do the left side, which the derivative of x is 1.
00:16
Leave x minus 6 cubed alone.
00:19
And then plus.
00:20
Now you leave x alone.
00:21
The derivative of the right side is the chain rule, where you move that 3 in front, and it's squared.
00:27
Now before i do the second derivative, i would actually factor out the x minus 6 squared, because it's shared between each of these.
00:36
And what i'm left with is an x minus 6.
00:40
That's, there's still one of those, plus this 3x here.
00:45
And in my head, well i'll go ahead and just do it.
00:49
It's x minus 6 squared times, what would that be? 4x minus 6.
00:54
So now the second derivative, the derivative of 4x minus 6 would be 4.
01:04
I'm leaving the other piece alone now.
01:06
And then plus, leave the 4x minus 6 alone, times the derivative of the other piece is 2x minus 6 to the first.
01:16
And again i would do some simplifying, but that's just me.
01:19
Matter of fact, you could have even factored out a 2 out of that if i wanted to.
01:24
So you could factor out a 4 and an x minus 6.
01:28
And what you're left with is an x minus 6 plus, remember i factored out a 2 out of that, so it's 2x minus 3.
01:35
I believe i've done everything i needed to...