Differentiate: f(x)=2(sin(2x))^2 with respect to x, and evaluate as a single trigonometric function.

f(x) = 2sin²(2x)Therefore, using the chain rule: f'(x)=2 x 2cos(2x) x 2sin(2x)(The 2 at the front arises from the constant 2, at the start of f(x), the 2cos(2x) comes from differentiating sin²(2x), then the 2sin(2x) comes from decreasing the original power of the sine function by 1 and multiplying by the constant in the function, 2)Therefore, f'(x)=6cos(2x)sin(2x)As we know 2sin(x)cos(x)=sin(2x) (double-angle formula), we can simplify f'(x) into f'(x)=3sin(4x)