If y = x sin x, Find \(\frac{d^2 y}{d^2 x}\)
A
2 cosx - x sinx
B
sinx + x cosx
C
sinx - x cosx
D
x sinx - 2 cosx
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
\(y = x \sin x\)
\(\frac{\mathrm d y}{\mathrm d x} = x \cos x + \sin x\)
\(\frac{\mathrm d^{2} y}{\mathrm d x^{2}} = x (- \sin x) + \cos x + \cos x\)
= \(2 \cos x - x \sin x\)
Source: Myschool Past Questions Archive (Record #31352)