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  4. If f(x)=x sin x, then f prime((π/2)) is equal to

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

Limits and Derivatives

Solution:

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