Differentiate f(x) = x sin(x)

In this question, we have the product of two separate terms, so we will choose to use the product rule for this question. Recall, for f(x) = u(x) v(x): f'(x) = u'(x) v(x) + u(x) v'(x). Here, we can set u(x) = x and v(x) = sin(x). Differentiating both terms with respect to x, we obtain u'(x) = 1 and v'(x) = cos(x). Using the product rule, this gives us:f'(x) = 1 * sin(x) + x cos(x) = sin(x) + x cos(x)