Answer
$f'(x)=cos(x)-xsin(x); f'(\frac{\pi}{4})=\frac{4\sqrt 2-\pi\sqrt 2}{8}$.
Work Step by Step
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) $
$f'(x)=(1)(cos(x))+(x)(-sin(x))=\cos(x)-x\sin(x)$
$f'(\frac{\pi}{4})=cos(\frac{\pi}{4})-(\frac{\pi}{4})(sin(\frac{\pi}{4}))=\frac{4\sqrt 2-\pi\sqrt 2}{8}$.
