Final answer:
To find the derivatives of the given functions, apply the chain rule and multiply the derivatives of the inner and outer functions.
Step-by-step explanation:
To find the derivatives of the given functions, we can use the chain rule. Let's start with the derivative of y = sin^2(x).
Step 1: Apply the chain rule to the outer function y = u^2: dy/du = 2u.
Step 2: Apply the derivative of the inner function u = sin(x): du/dx = cos(x).
Step 3: Multiply the derivatives from steps 1 and 2 to get the final result: dy/dx = 2u * cos(x) = 2sin(x) * cos(x).
Similarly, for the function y = 2cos^2(x), the derivative is dy/dx = -4sin(x) * cos(x).