Put u = 2x + 3 and v = sin 4x

Now

`(dv)/(dx)=4\ cos 4x`

So using the quotient rule, we have:

`(dy)/(dx) =(v(du)/(dx)-u(dv)/(dx))/v^2`

`=((sin 4x)(2)-(2x+3)(4\ cos 4x))/(sin^2 4x)`

`=(2\ sin 4x-4(2x+3)cos 4x)/(sin^2 4x)`