# Mark the Correct Alternative in of the Following: If F(X) = X Sinx, Then F ′ ( π 2 ) = - Mathematics

MCQ

Mark the correct alternative in of the following:

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

#### Options

• 1

• −1

• $\frac{1}{2}$

#### Solution

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).

Concept: The Concept of Derivative - Algebra of Derivative of Functions
Is there an error in this question or solution?

#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 30 Derivatives
Q 12 | Page 48