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隐函数y=1+xe^y的二阶导数
人气:280 ℃ 时间:2019-08-26 06:44:31
解答
两边对x求导:y'=e^y+xe^y* y'得:y'=e^y/(1-xe^y)=(y-1)/x/(1-y+1)=(y-1)/[x(2-y)]y"=[y'x(2-y)-(y-1)(2-y-xy')]/[x^2(2-y)^2]=[(y-1)-(y-1)(2-y-(y-1)/(2-y)]/[x^2(2-y)^2]=(y-1)^2(3-y)/[x^2(2-y)^3]
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