Chain rule:
If y = f(t) and t = g(x) then dy/dx = dy/dt x dt/dx
d/dx sin2 (2x + 3) = 2 sin (2x + 3) * d/dx {sin(2x + 3)}
= 2 sin (2x + 3) * cos(2x + 3) * d/dx (2x + 3)
= 2 sin (2x + 3) * cos (2x + 3) * 2
= 4 sin (2x + 3) cos (2x + 3)
= 2 sin (4x + 6)
[Using identity: 2sin x cos x = sin 2x]