Question

Differentiate the functions given in Exercises.
$\cos x.\cos 2x.\cos 3x$.

Answer 1

$\cos x\cos 2x\cos 3x\cos \left(2{\cos }^{2}x-1\right)\cos 3x=(2{\cos }^{3}x-\cos x)\cos 3xd{f}^{{}^{\prime }}\left(x\right)=\cos 3x\frac{d}{dx}(2{\cos }^{3}x-\cos x)+\frac{d}{dx}\left(\cos 3x\right)(2\cos 3x-\cos x)=\cos 3x(6{\cos }^{2}x-(-\sin x))+\sin x+3(-\sin 3x)\left(2{\cos }^{2}x-\cos x\right)=\sin x\cos 3x-6{\cos }^{2}x\sin x\cos 3x-3\sin 3x\cos x$