设函数y=f(x+y),其中f具有二阶导数,求二阶导数

2024-10-28 12:31:50
推荐回答(2个)
回答1:

简单计算一下即可,答案如图所示

回答2:

设u=x+y,则y=f(x+y)=f(u) y'=dy/dx=df/dudu/dx=f'(u)u'=f'(u)(1+y')。所以有
y'=f'(x+y)(1+y') 所以:y'=f'(x+y)/(1-f'(x+y))
y"=d(f'(x+y)(1+y'))/dx
=f"(x+y)(1+y')²+f'(x+y)y"
y"=(f"(x+y)(1+y')²)/(1-f'(x+y))
=f"(x+y)/(1-f'(x+y))³