Question

Mark the correct alternative in of the following: 

If f(x) = x sinx, then \[f'\left( \frac{\pi}{2} \right) =\] 

विकल्प

• 0 

• 1            

• −1 

• \[\frac{1}{2}\] 

Answer 1

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

\[f'\left( x \right) = x \times \frac{d}{dx}\left( \sin x \right) + \sin x \times \frac{d}{dx}\left( x \right) \left( \text{ Product rule } \right)\]
\[ = x \times \cos x + \sin x \times 1\]
\[ = x \cos x + \sin x\] 

Putting \[x = \frac{\pi}{2}\] 

 we get \[f'\left( \frac{\pi}{2} \right) = \frac{\pi}{2} \times \cos\left( \frac{\pi}{2} \right) + \sin\left( \frac{\pi}{2} \right)\]
\[ = \frac{\pi}{2} \times 0 + 1\]
\[ = 1\]

Hence, the correct answer is option (b).