y=(sin x)^lnx 对数求导

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/03 21:11:00
y=(sin x)^lnx 对数求导

y=(sin x)^lnx 对数求导
y=(sin x)^lnx 对数求导

y=(sin x)^lnx 对数求导
y = (sinx)^lnx
lny = (lnx) ln(sinx)
(1/y) y' = (lnx) (1/sinx) cosx + (ln(sinx)) 1/x
= (lnx) cotx + (1/x) lin(sinx)
y' = [(lnx) cotx + (1/x) lin(sinx)]y
= [(lnx) cotx + (1/x) lin(sinx)]((lnx) cotx + (1/x) lin(sinx))

(sinX求导*linX)+(sinx*linx的导数)=cosx*linx+sinx*1/X