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

The product rule states that (uv)' = u'v + uv' Therefore we know that to find dy/dx we must have (sin(2x))'(4x+1)^3 +sin(2x)((4x+1)^3)' We can differentiate sin(2x) to 2cos(2x) and using the chain rule we can differentiate (4x+1)^3 to 12(4x+1)^2 Therefore our answer is 12sin(2x)(4x+1)^2 + 2cos(2x)(4x+1)^3