这几题的二阶导数怎么求,求帮忙,谢谢!

要有过程,谢谢大家!
2025-04-02 10:58:54
推荐回答(4个)
回答1:

方法如下,
请作参考:

回答2:

朋友,您好!详细完整清晰过程rt,希望能帮到你

回答3:

(2)

(f(x^2))'

链式法则

=f'(x^2) . (x^2)'

=f'(x^2) . (2x)

=2x.f'(x^2)

(f(x^2))''

2阶导数=1阶导数再求导数

=((f(x^2))')'

=(2x.f'(x^2))'

链式法则

=2[ x.【f'(x^2)】' + f'(x^2). (x)']
=2[ x f''(x^2).(x^2)' + f'(x^2)]

=2[ x f''(x^2).(2x) + f'(x^2)]


=2[ 2x^2. f''(x^2) + f'(x^2)]

回答4:

解1. f(x)=[e^(-x)]sinx,
f'(x)=[e^(-x)]'sinx+[e^(-x)](sinx)'
=-[e^(-x)]sinx+[e^(-x)]cosx=[e^(-x)](cosx-sinx)
f''(x)=[e^(-x)]'(cosx-sinx)+[e^(-x)](cosx-sinx)'=-[e^(-x)](cosx-sinx)+[e^(-x)](-sinx-cosx)
=[e^(-x)](sinx-cosx-sinx-cosx)=-2[e^(-x)]cosx