Posted by Amanda on Tuesday, November 3, 2009 at 5:41pm.
Use the chain rule:
d(f(u(x))/dx=df/du.du/dx
d(cos²(4x))/dx
=2cos(4x)d(cos(4x))/dx
=2cos(4x)(-sin(4x))d(4x)/dx
=2cos(4x)(-sin(4x))(4)
=-8sin(4x)cos(4x)
=-4sin(8x)
The last simplification may not be required or recognized by a computerized answer.