Question

Mark the correct alternative in of the following: 

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

Options

• 0 

• 1            

• −1 

• $$\frac{1}{2}$$ 

Answer 1

f(x) = x sinx
Differentiating both sides with respect to x, we get 

$$f^{\prime }\left(x\right)=x\times \frac{d}{dx}(\sin x)+\sin x\times \frac{d}{dx}\left(x\right)\left(\text{ Product rule }\right)$$
$$=x\times \cos x+\sin x\times 1$$
$$=x\cos x+\sin x$$ 

Putting $$x=\frac{\pi }{2}$$ 

 we get $$f^{\prime }\left(\frac{\pi }{2}\right)=\frac{\pi }{2}\times \cos \left(\frac{\pi }{2}\right)+\sin \left(\frac{\pi }{2}\right)$$
$$=\frac{\pi }{2}\times 0+1$$
$$=1$$

Hence, the correct answer is option (b).