MCQ

Mark the correct alternative in of the following:

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

#### Options

0

1

−1

\[\frac{1}{2}\]

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#### Solution

*f*(*x*) = *x* sin*x*

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).

Concept: The Concept of Derivative - Algebra of Derivative of Functions

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