A) \[{{2}^{2}}(\cos 2x+{{2}^{2}}\cos 4x)\]
B) \[{{2}^{2}}(\cos 2x-{{2}^{2}}\cos 4x)\]
C) \[{{2}^{2}}(-\cos 2x+{{2}^{2}}\cos 4x)\]
D) \[-{{2}^{2}}(\cos 2x+{{2}^{2}}\cos 4x)\]
Correct Answer: D
Solution :
\[y=2\cos x\cos 3x\] \[\frac{dy}{dx}=2\cos x\,.\,(-3\sin 3x)+2\cos 3x(-\sin x)\] \[=\,-3(\sin 4x+\sin 2x)+(-1)[\sin 4x+\sin (-2x)]\] \[\frac{{{d}^{2}}y}{d{{x}^{2}}}=-3(4\cos 4x+2\cos 2x)-1(4\cos 4x-2\cos 2x)\] \[=-16\cos 4x-4\cos 2x\]\[=-4(\cos 2x+4\cos 4x)\] \[=-{{2}^{2}}(\cos 2x+{{2}^{2}}\cos 4x)\].
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