00:01
What is the derivative of f of x equals x squared plus two cosine squared x? i'll split it up into two parts.
00:08
We can do that whenever we see a plus sign or a minus sign.
00:12
So we've got the x squared in the front and the two cosine squared x in the back.
00:18
We'll start with the green underline part.
00:20
This is the power rule.
00:22
So you bring the exponent down to x and then you subtract one from the exponent.
00:29
So you just have to the first part, which we don't need to put.
00:32
So that's 2x.
00:34
Then we have our trigonometric part, which is the new information that we're working on.
00:39
This is where it gets complicated.
00:41
So writing cosine squared x is also like writing cosine x squared.
00:49
So this is where you have to use the chain rule.
00:54
So we keep the two out front.
00:57
We bring this down using the power rule.
00:59
So it's like saying 2 cosine x and then 2 minus 1 is just to the first power.
01:08
So 2 cosine x.
01:10
But then we have to take the derivative of what's inside as well.
01:16
That's using the chain rule...