y = (x^2)sin(3x). Find dy/dx

We need to differentiate x²sin(3x). We know how to differentiate (x²) on its own, and how to differentiate sin(3x) on its own. So we can use the Product rule:

dy/dx = (d/dx(x²))sin(3x) + x²(d/dx(sin(3x))

          = (2x)sin(3x) + x²(3cos(3x))

          = 2xsin(3x) + 3x²cos(3x)