Calculus (derivatives)
posted by Amanda .
Find the derivative of
cos^2(4x)

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.