## Calculus 10th Edition

$y'=4x\cos(x)+(2-x^2)\sin(x)$.
$y=f(x)+g(x)\rightarrow f(x)=2x\sin(x)$; $g(x)=x^2cos(x)$ Using Product Rule: $f'(x)=((u(x)(v(x))’=u’(x)v(x)+u(x)v’(x))$ $u(x)=2x ;u’(x)=2$ $v(x)=\sin(x) ;v’(x)=\cos(x)$ $f'(x)=2x\cos(x)+2\sin(x)$. Using Product Rule: $g'(x)=((u(x)(v(x))’=u’(x)v(x)+u(x)v’(x))$ $u(x)=x^2 ;u’(x)=2x$ $v(x)=\cos(x) ;v’(x)=-\sin(x)$ $g'(x)=(2x)(\cos(x))-x^2\sin(x)$. Using Sum Rule: $y'=f'(x)+g'(x)=4x\cos(x)+(2-x^2)\sin(x)$.