Answer
$h'(x)=\dfrac{\sin{x}+2x\cos{x}}{2\sqrt{x}}.$
Work Step by Step
Product Rule $(h’(x)=(u(x)(v(x))’=u’(x)v(x)+u(x)v’(x))$
$u(x)=\sqrt{x} ;u’(x)=\dfrac{1}{2\sqrt{x}} $
$v(x)=\sin{x} ;v’(x)=\cos{x} $
$h'(x)=(\dfrac{1}{2\sqrt{x}})(\sin{x})+(\cos{x})(\sqrt{x})$
$=\dfrac{\sin{x}+2x\cos{x}}{2\sqrt{x}}$
