y = sin(2x)
If you differentiate sin(x), you get cos(x).
So, if you differentiate sin(u) you will get cos(u).
Then let u = 2x.
Since u = 2x, then du/dx = 2.
And dy/dx = (dy/du)*(du/dx).
Now, y = sin(u), with dy/du = cos(u).
So, dy/dx = (dy/du)*(du/dx) = cos(u)*2
i.e. dy/dx = 2cos(2x)