Differentiate y = x sin(x)

The question is asking to differentiate which means find dy/dx. If we think about the differentiation rules we know about, we see that we should use the product rule as y is a product (multiplication) of two basic functions, x and sin(x). If y = uv then by the product rule, dy/dx = u'(x).v(x) + u(x).v'(x).In our particular question, u(x) = x and v(x) = sin(x). We know that the derivative of sin(x) is cos(x). So:dy/dx = 1.sin(x) + x.cos(x) = sin(x) + x.cos(x).