Question

关于高阶求导的问题 帮帮忙！！！

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Answer 1

dx/dy = 1/y'

d^2 x/dy^2
= d(1/y')/dy
= [-dy'/(y')^2]/dy
= -dy'/[(y')^2 dy]
= -(dy'/dx)/[(y')^2 (dy/dx)]
= -y''/(y')^3

d^3 x/dy^3
= d(-y''/(y')^3)/dy
= { [y''d[(y')^3] - d(y'')(y')^3] /(y')^6 } /dy
= { [3y''(y')^2dy' - d(y'')(y')^3] /(y')^6 } /dy
= { [3y''(y')^2(dy'/dx) - [d(y'')/dx](y')^3] /(y')^6 } /[dy/dx]
= { [3(y'')^2(y')^2 - y'''(y')^3] /(y')^7
= [ 3(y'')^2 - y'''y' ] /(y')^5