对y=(cosx)^x求导数.题目是y等于cosx的x次方

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对y=(cosx)^x求导数.题目是y等于cosx的x次方
对y=(cosx)^x求导数.
题目是y等于cosx的x次方

对y=(cosx)^x求导数.题目是y等于cosx的x次方
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

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