y = [cos(x)]^x = e^[xlncos(x)],
y' = e^[xlncos(x)]*[xlncos(x)]' = e^[xlncos(x)]*[lncos(x) + x/cos(x)*(cos(x))']
= e^[xlncos(x)]*[lncos(x) + x/cos(x)*(-sin(x))]
= e^[xlncos(x)]*[lncos(x) - xtan(x)]
= [lncos(x)-xtan(x)]*[cos(x)]^x