隐函数求导:y+iny=x确定隐函数y=y(x),求y'和y''.

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隐函数求导:y+iny=x确定隐函数y=y(x),求y'和y''.
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隐函数求导:y+iny=x确定隐函数y=y(x),求y'和y''.
隐函数求导:y+iny=x确定隐函数y=y(x),求y'和y''.

隐函数求导:y+iny=x确定隐函数y=y(x),求y'和y''.
y+lny=x,两边对x求导数:y'+(1/y)*y'=1,所以:y'=y/(y+1)
对y'两边求对x的导数:y''=(y'*(y+1)-y*y')/(y+1)^2=y'/(y+1)^2=y/(y+1)^3

两边x求导:y'+(1/y)y'=1,y'=y/(y+1),同理对上式求导得y''+(y''y-(y')^2)/y^2=0,再代如上式y'=...得y''=y/(y+1)^3