Question

数学题，对y=（cosx）^x求导数。

题目是y等于cosx的x次方
课本后面有答案，我要解题过程。提高悬赏。

Answer 1

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

Answer 2

y=（cosx）^x
y'=Cos[x]^x (Log[Cos[x]] - x Tan[x])