Question Detail
Question
Using first principle, evaluate Δy/Δx of the derivative of cos(3x)
Correct Answer
Option C is the correct answer.
Detailed Explanation
Using cosA-cosB=-2sin((A+B)/2)sin((A-B)/2) with A=3(x+Δx), B=3x: Δy=cos3(x+Δx)-cos3x=-2sin(3x+3Δx/2)sin(3Δx/2). Dividing by Δx gives option C.
Hint
Apply the sum-to-product identity for the difference of two cosines.