Differentiate, y=sin4xcos7x

$y= \sin 4x\ \cos 7x=\frac{1}{2} \cdotp 2\sin 4x\cos 7x$ 

$y=\frac{1}{2}(\sin 11x-\sin 3x)$ 

differentiating with respect  to $x$ 

$\frac{dy}{dx} = \frac{1}{2}\left[\frac{d}{dx}(\sin 11x-\sin 3x)\right]$ 

$= \frac{1}{2}\left[\cos 11x\cdotp \frac{d}{dx}( 11x) -\cos 3x\cdotp \frac{d}{dx}( 3x)\right]$ 

$=\frac{1}{2}[ 11\cos 11x-3\cos 3x]$