If f(x) = √(1-sin(2x)) , then f'(x) is equal to f(x) = √(1-sin(2x))

Using the trigonometric identity  to solve the given problem:-

Such as:

sin²x +cos²x =1

sin(2x) = 2 sin(x)cos(x)

If f(x) = √(1-sin(2x)) , then f'(x) = -(cosx+sinx) for x∈(0,Π/4).

Hence Option(C) is the correct option.