Question

设由方程x+2y+z=e^(x-y-z)确定的隐函数为z=z(x,y),求d^2z/dx^2

Answer 1

x+2y+z=e^(x-y-z)两边对x求偏导注意到z=z(x,y)
1+z'=e^(x-y-z)*(1-z')...(1)
再对x求偏导
z"=e^(x-y-z)(1-z')^2-z"e^(x-y-z)...(2)
(1)可把z'解出代入(2)
即可得z"=d^2z/dx^2 =...