Final answer:
The derivatives of the given functions y = cos(3x²), y = cos(3x)², and y = cos²(x), are found using the chain rule and trigonometric identities to be -6x sin(3x²), -6 cos(3x) sin(3x), and -sin(2x) respectively.
Step-by-step explanation:
To find the derivative of the given functions, we will use the chain rule and the trigonometric identities.
- For y = cos(3x²), the derivative is:
- For y = cos(3x)², the derivative is:
- For y = cos²(x), the derivative is:
Each function requires the application of the chain rule where we differentiate the outer function and then multiply by the derivative of the inner function.