Given that y = (( 4x + 1 )^3)sin(2x), find dy/dx.

This is an example of the chain rule.

The chain rule is the following: if y = uv, then dy/dx = udv/dx + vdu/dx

So in this case, u = ( 4x + 1)^3, v = sin(2x)

du/dx = (3)(4)( 4x + 1 )^2, dv/dx = 2cos(2x)

dy/dx = (12( 4x + 1)^2)sin(2x) + 2(( 4x + 1)^3)cos(2x)