方法如下,
请作参考:
朋友,您好!详细完整清晰过程rt,希望能帮到你
(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)]
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