Differentiate the function \( y = \cos x \cdot \cos 2x \cdot \cos 3x \) with respect to \( x \).

A
\( -(\sin x + 2\sin 2x + 3\sin 3x) \)
B
\( \sin x \sin 2x \sin 3x \)
C
\( \cos x \cos 2x \sin 3x \)
D
\( -(\sin x \cos 2x \cos 3x + 2\cos x \sin 2x \cos 3x + 3\cos x \cos 2x \sin 3x) \)

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Correct answer · Option D

\( -(\sin x \cos 2x \cos 3x + 2\cos x \sin 2x \cos 3x + 3\cos x \cos 2x \sin 3x) \)

Apply the product rule for three functions: \( \frac{d}{dx}(uvw) = u'vw + uv'w + uvw' \).