To find the second derivative of \(y = x \sin x\), we'll need to differentiate twice with respect to \(x\). Let's start by finding the first derivative and then the second derivative.

Given \(y = x \sin x\), we'll use the product rule for differentiation:

First derivative:

\(\frac{dy}{dx} = \frac{d}{dx}(x) \cdot \sin x + x \cdot \frac{d}{dx}(\sin x)\)

\(\frac{dy}{dx} = \sin x + x \cos x\)

Now, let's find the second derivative:

\(\frac{d^2y}{dx^2} = \frac{d}{dx}(\sin x + x \cos x)\)

Using the sum rule and the product rule:

\(\frac{d^2y}{dx^2} = \frac{d}{dx}(\sin x) + \frac{d}{dx}(x \cos x)\)

\(\frac{d^2y}{dx^2} = \cos x - x \sin x + \cos x\)

\(\frac{d^2y}{dx^2} = 2 \cos x - x \sin x\)