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