If y = x Sin x, find \(\frac{dy}{dx}\) when x = \(\frac{\pi}{2}\)
A
\(\frac{- \pi}{2}\)
B
-1
C
1
D
\(\frac{ \pi}{2}\)
Verified Correct Answer: C.
Step-by-Step Mathematical Solution
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 + \(\frac{\pi}{2}\) \times 0
= 1
Source: Myschool Past Questions Archive (Record #46327)