Final answer:
The 30th derivative of y = cos(2x) is -4^15cos(2x).
Step-by-step explanation:
To find the 30th derivative of y = cos(2x), we can use the chain rule repeatedly. The derivative of cos(2x) is -2sin(2x), and we can differentiate sin(2x) to get -4cos(2x). By continuing this process, we can see that the 30th derivative will be the same as the 28th derivative, which is -4^(30/2)cos(2x). Therefore, the 30th derivative of y = cos(2x) is -4^15cos(2x).