By applying the Product Rule [d/dx(uv) = u'v + uv'], where u = x and v = sin(x). Here u' = 1 and v' = cos(x). Thus, f'(x) = (1)sin(x) + (x)cos(x). Option A and D are incorrect because they only differentiated one part of the product. Option C is incorrect because it uses the wrong sign (subtraction instead of addition).