00:01
So given this function, there's a couple ways to think about how to find the derivative of this function.
00:06
The first thing i would think about, okay, i have 2 times sine of the same angle times cosine at the same angle.
00:11
This is very similar to the sine double angle form.
00:15
A sine of 2x is 2, sine of x times cosine of x.
00:19
So then i could rewrite this function as this is 2 times sine of 2x, or this will be 2 times sine of 4x.
00:32
Then i could just find the derivative here, right? what's the derivative of sine? derivative sign is cosine.
00:39
Keep the constant.
00:40
So this will be cosine of 4x.
00:43
Since i have a 4 inside of that, derivative of 4x, chain rule is going to be 4.
00:49
So one way to write this would be 2 times 4, 8, cosine of 4x.
00:56
Or another way i could do this is i could just use...