Question

If $f\left(x\right)=x\sin x,$ find $f^{\prime }\left(\pi \right)$, using first principle.

Answer 1

Given,

$f\left(x\right)=x\sin x$

$f^{\prime }\left(x\right)=\sin x+x\cos x$

$f^{\prime }\left(\pi \right)=\sin \pi +\pi \cos \pi$

$=0+\pi (-1)$

$\therefore f^{\prime }\left(\pi \right)=-\pi$