Question

If $f\left(x\right)=xsinx$, then $f^{\prime }\left(\frac{\pi }{2}\right)=$

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

Answer 1

The correct option is B

1

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

Differentiating both sides with respect to x, we get

$f^{\prime }\left(x\right)=x\times \frac{d}{dx}\left(sinx\right)+sinx\times \frac{d}{dx}\left(x\right)$ (Product rule)

$=x\times cosx+sinx\times 1=xcosx+sinx$

$\text{Putting}x=\frac{\pi }{2},\text{we get}$

$f^{\prime }\left(\frac{\pi }{2}\right)=\frac{\pi }{2}\times cos\left(\frac{\pi }{2}\right)+sin\left(\frac{\pi }{2}\right)$

$=\frac{\pi }{2}\times 0+1$

$=1$