Given that y=((4x+1)^3)sin2x. Find dy/dx.

To answer this we will need to use the product rule which is as follows: For y=uv, dy/dx=u'v+uv' where u' is the derivative of u and v' is the derivative of v.

In this case, u= (4x+1)^3 and v= sin2x. u'= 34(4x+1)^2 = 12*(4x+1)^2 and v'= 2cos2x. Therefore dy/dx= u'v+uv'= (12*(4x+1)^2)sin2x + 2((4x+1)^3)*cos2x.