Answer
$y'=x\cos(x)$
Work Step by Step
$y=f(x)+g(x)\rightarrow f(x)=x\sin(x)$; $g(x)=\cos(x)$
Product Rule $f'(x)=((u(x)(v(x))’=u’(x)v(x)+u(x)v’(x))$
$u(x)=x ;u’(x)=1 $
$v(x)=\sin(x) ; v’(x)=\cos(x) $
$f'(x)=\sin(x)+x\cos(x)$
$g'(x)=\dfrac{d}{dx}(\cos(x))=-\sin(x)$
$y'=f'(x)+g'(x)=x\cos(x)$
