Question

d/dx (4ln) (2x)sin2x using product rule

Answer 1

The way you typed it, I will read it as

[ 4ln(2x)][sin 2x]

so derivative is
(4ln(2x))(2)(cos 2x) + sin 2x (4/(2x) (2)
= 8ln(2x) cos(2x) + 4sin(2x) /x