Question Detail
Question
If \( f(x) = \sin^2(3-x) \), find \( f'(0) \).
Correct Answer
Option B is the correct answer.
Detailed Explanation
Apply chain rule: ( f'(x) = 2\sin(3-x) \cdot \frac{d}{dx}(\sin(3-x)) = 2\sin(3-x) \cdot \cos(3-x) \cdot (-1) ). At ( x=0 ), ( f'(0) = -2\sin 3 \cos 3 ).
Hint
Differentiate the outer power, then the sine, then the inside function.