Final answer:
To find g'(x), use the product rule to differentiate x * sin(x). To find g''(x), differentiate g'(x) using the product rule again.
Step-by-step explanation:
To find the first derivative of the function g(x) = x sin(x), we can use the product rule. The product rule states that if you have two functions multiplied together, the derivative of the product is the first function times the derivative of the second function plus the second function times the derivative of the first function. Applying this rule to g(x), we have g'(x) = x * cos(x) + sin(x).
To find the second derivative, we can differentiate g'(x) using the product rule again. We have g''(x) = cos(x) - x * sin(x) + cos(x).