函数y=sin6(62x2+73x+14)的导数计算

函数y=sin6(62x2+73x+14)的导数计算主要内容：本文主要用复合函数求导法则、链式求导法则以及取对数求导等方法，介绍计算函数y=sin6(62x2+73x+14)一阶和二阶导数的步骤。※.复合函数链式求导计算一阶导数由复合函数求导法则，对x求导有：dydx=6*sin2(62x2+73x+14)*cos(62x2+73x+14)*(62x2+73x+14)'，=6*sin2(62x2+73x+14)*cos(62x2+73x+14)*(124x+73),=6(124x+73)*sin2(62x2+73x+14)*cos(62x2+73x+14).※.取对数求导计算一阶导数首先对方程两边取对数，有：lny=lnsin6(62x2+73x+14),lny=6lnsin(62x2+73x+14),方程两边同时对x求导，有：y'y=6[sin(62x2+73x+14)]'sin(62x2+73x+14),y'y=6[cos(62x2+73x+14)](124x+73)sin(62x2+73x+14),y'=sin6(62x2+73x+14)*6[cos(62x2+73x+14)](124x+73)sin(62x2+73x+14),y'=sin2(62x2+73x+14)*6[cos(62x2+73x+14)](124x+73),=6(124x+73)sin2(62x2+73x+14)*cos(62x2+73x+14).※.二阶导数计算本处根据函数特征，采取取对数计算导数，首先对函数两边同时取对数，有：lny'=ln6(124x+73)sin2(62x2+73x+14)*cos(62x2+73x+14),则：lny'=ln6+ln(124x+73)+5lnsin(62x2+73x+14)+lncos(62x2+73x+14),对方程两边同时对x再次求导，y''y'=124124x+73+5[sin(62x2+73x+14)]'sin(62x2+73x+14)+[cos(62x2+73x+14)]'cos(62x2+73x+14),=124124x+73+5cos(62x2+73x+14)(124x+73)sin(62x2+73x+14)-sin(62x2+73x+14)(124x+73)cos(62x2+73x+14)=124124x+73+5(124x+73)ctg(62x2+73x+14)-(124x+73)tan(62x2+73x+14),则：y''=6(124x+73)sin2(62x2+73x+14)*cos(62x2+73x+14)[124124x+73+5(124x+73)ctg(62x2+73x+14)-(124x+73)tan(62x2+73x+14)],=744sin2(62x2+73x+14)*cos(62x2+73x+14)+30(124x+73)2sin4(62x2+73x+14)*cos2(62x2+73x+14)-6(124x+73)2sin6(62x2+73x+14),=372sin4(62x2+73x+14)*sin(124x2+146x+28)+30(124x+73)2sin4(62x2+73x+14)*cos2(62x2+73x+14)-6(124x+73)2sin6(62x2+73x+14)。