Differentiation Question 389
Question: $ \frac{d^{2}}{dx^{2}}(2\cos x\cos 3x)= $
[RPET 2003]
Options:
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) $
Show Answer
Answer:
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}{dx^{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) $ .
BETA
