y=e^[tan(1⼀x)] 求导数

需要过程，谢谢

2025-12-17 15:03:51

推荐回答（4个）

回答1：

y'=e^[tan(1/x)]*[tan(1/x)]'
=e^[tan(1/x)]*[sec(1/x)]^2*(1/x)'
=-{e^[tan(1/x)]*[sec(1/x)]^2}/x^2

回答2：

y'=e^[tan(1/x)]*[tan(1/x)]'=e^[tan(1/x)]*[sec(1/x)]^2*(1/x)'=-{e^[tan(1/x)]*[sec(1/x)]^2}/x^2

回答3：

y=(e^tan(1/x))'
=e^tan(1/x)*[tan(1/x)]'
=e^tan(1/x)*{1/[(cos(1/x))^2]}*(1/x)'
=e^tan(1/x)*{1/[(cos(1/x))^2]}*(-1/x^2)'

回答4：

y=e^[tan(1/x)]

y'=e^[tan(1/x)]*[tan(1/x)]'

=e^[tan(1/x)]*[sec(1/x)]^2*(1/x)'

=e^[tan(1/x)*[sec(1/x)]^2*(-1/x^2)