00:01
So for this question, we're asked to find the derivative of this function outlined here in black.
00:08
And because we have multiple functions being multiplied together, we have to use the product rule.
00:14
So our first step is we're going to want to group together our sign and cosine functions and do a product rule based on these two functions here.
00:25
So we'll set a equal to cosine of x and then a prime.
00:31
Will equal negative sign of x, and we'll have b equals sign of x, and b prime equaling cosine of x.
00:44
So if we do the product rule for this first section, we'll have negative sign of x times sine of x plus cosine of x times cosine of x.
01:03
And when we simplify this, we get cosine squared of x minus sine squared of x, and this equals cosine of 2x.
01:19
This is a double angle trick identity.
01:22
So make sure you have your trick identity worksheet on the side...
