Question

If $f(x)=x\sin x$, then $f^{\prime }\left(\frac{\pi }{2}\right)$ is equal to

• A. 0
• B. 1
• C. $-1$
• D. $\frac{1}{2}$

Answer 1

Answer: (B)

$\because f(x)=x\sin x$
$\Rightarrow f^{\prime }(x)=\frac{d}{dx}(x\sin x)$
$=\sin x\frac{d}{dx}x+x\frac{d}{dx}\sin x=\sin x+x\cos x$
$\Rightarrow f^{\prime }\left(\frac{\pi }{2}\right)=\sin \frac{\pi }{2}+\frac{\pi }{2}\cos \frac{\pi }{2}=1$