设函数y=f(x+y) ,其中f具有二阶导数,且f'不等于1,求二阶导数

Question

如题所述

Answer 1

简单计算一下即可，答案如图所示

Answer 2

设函数y=f(x+y)
,其中f具有二阶导数,且f'不等于1,求二阶导数
y=f(x+y)
则：
y'=f'(x+y)*(1+y')=f'(x+y)+f'(x+y)*y'
===>
[1-f'(x+y)]*y'=f'(x+y)
===>
y'=f'(x+y)/[1-f'(x+y)]
所以：
y''={f''(x+y)*(1+y')*[1-f'(x+y)]-f'(x+y)*[-f''(x+y)*(1+y')]}/[1-f'(x+y)]^2
=f''(x+y)*(1+y')/[1-f'(x+y)]^2
=f''(x+y)*[1/1-f'(x+y)]/[1-f'(x+y)]^2
=f''(x+y)/[1-f'(x+y)]^3.