求隐函数y=sin(x+y)的二阶导数
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对y=sin(x+y)的等式两边对x求一阶导y'=cos(x+y)×(1+y')y'=cos(x+y)/[1-cos(x+y)]y''=y''cos(x+y)-(1+y')²sin(x+y)y''[cos(x+y)-1]=(1+y')²sin(x+y)=sin(x+y)/[1-cos(x+y)]²则y''=sin(x+y)/[1-cos(x+y)]³
咨询记录 · 回答于2022-10-20
求隐函数y=sin(x+y)的二阶导数
对y=sin(x+y)的等式两边对x求一阶导y'=cos(x+y)×(1+y')y'=cos(x+y)/[1-cos(x+y)]y''=y''cos(x+y)-(1+y')²sin(x+y)y''[cos(x+y)-1]=(1+y')²sin(x+y)=sin(x+y)/[1-cos(x+y)]²则y''=sin(x+y)/[1-cos(x+y)]³
对y=sin(x+y)的等式两边对x求一阶导y'=cos(x+y)×(1+y'),化简得y'=cos(x+y)/[1-cos(x+y)]对y'=cos(x+y)×(1+y')两边再求导y''=y''cos(x+y)-(1+y')²sin(x+y)y''[cos(x+y)-1]=(1+y')²sin(x+y)=sin(x+y)/[1-cos(x+y)]²则y''=sin(x+y)/[cos(x+y)-1]³
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