If y = x sin x, Find \(\frac{d^2 y}{d^2 x}\)
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Correct Answer: Option A
Explanation:
\(y = x \sin x\)
\(\frac{\mathrm d y}{\mathrm d x} = x \cos x + \sin x\)
\(\frac{\mathrm d^{2} y}{\mathrm d x^{2}} = x (- \sin x) + \cos x + \cos x\)
= \(2 \cos x - x \sin x\)
\(y = x \sin x\)
\(\frac{\mathrm d y}{\mathrm d x} = x \cos x + \sin x\)
\(\frac{\mathrm d^{2} y}{\mathrm d x^{2}} = x (- \sin x) + \cos x + \cos x\)
= \(2 \cos x - x \sin x\)