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If y = x Sin x, find $\frac{dy}{dx}$ when x = \(\frac{\pi}...

If y = x Sin x, find $\frac{dy}{dx}$ when x = $\frac{\pi}{2}$

A.

$\frac{- \pi}{2}$

B.

-1

C.

1

D.

$\frac{ \pi}{2}$

View answer & explanation

Correct answer is C

y = xsinx

$\frac{dy}{dx}$ = $1 \sin x + x \cos x$

= $\sin x + x \cos x$

At x = $\frac{\pi}{2}$

= sin $\frac{\pi}{2}$ + $\frac{\pi}{2} \cos {\frac{\pi}{2}}$

= 1 + $\frac{\pi}{2}$ × 0

= 1

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