00:01
Asked us to find the derivative of a very complex function.
00:05
So to start, we're going to look at our function, f of w is equal to cosine of sine of 2w.
00:17
So our most outer layer is the cosine.
00:21
The next inner layer is the sine in this case.
00:35
So first off, we need to look at the derivative of cosine and finding f prime of w.
00:42
So the derivative of cosine of something is equal to negative sign of whatever was inside.
00:51
In our case, it would be sine inverse of 2w.
00:57
By the chain rule, we have to multiply this by the derivative of the inside.
01:02
So the derivative of sine inverse of something is given by this formula 1 over the square root of 1 minus whatever was inside squared.
01:18
What's inside of our sine inverse, that is equal to 2w.
01:24
Now, we're almost done, but not yet.
01:27
We still have to evaluate the chain rule for the second time.
01:31
So what's inside of our parentheses is 2w.
01:34
Well, the derivative of that would just be 2...