Question

find the derivatives
1. y=sin^3(2x)(cos2x)

Answer 1

There is only one derivative of a function. I assume that you mean
y = sin^3(2x)*cos(2x)
Treat that as the product of two functions u and v, and use the rule
d/dx(u*v) = u dv/dx + v du/dx

u = sin^3(2x)
du/dx = 6 sin^2(2x)*cos(2x)
(I had to use the 'function of a function' rule twice for that one)

v = cos(2x)
dv/dx = -2 sin(2x)

Now put it all together.