If \(y = \cos^{3}(2x)\), then \(\displaystyle\frac{dy}{dx}\) is equal to
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(-6\cos^{2}(2x)\sin(2x)\)
The chain rule works from the outside in: the cube, then cosine, then 2x.
\( \displaystyle \frac{dy}{dx} = 3\cos^{2}(2x) \cdot (-\sin 2x) \cdot 2 \)
\( = -6\cos^{2}(2x)\sin(2x) \)