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dx/dy =1/y'
d^x/dy^2
=d/dy (1/y')
=d/dx (1/y') / (dy/dx)
=d/dx (1/y') / y'
= [-y''/(y')^2]/y'
=-y''/(y')^3
d^x/dy^2
=d/dy (1/y')
=d/dx (1/y') / (dy/dx)
=d/dx (1/y') / y'
= [-y''/(y')^2]/y'
=-y''/(y')^3
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追答
dx/dy = 1/(dy/dx) = 1/y'
d^2x/dy^2
=d/dy ( dx/dy)
=d/dy (1/y')
=d/dx (1/y') . dx/dy (链式法则)
=d/dx (1/y') /y'
=[-y''/(y')^2 ] /y'
=-y''/(y')^3
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