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咨询记录 · 回答于2022-06-28
求函数z=sin2/x-x3y2+2的二阶偏导数
求函数z=sin2/x-x3y2+2的二阶偏导数解:dz/dx=2xcos(x²-2y)d²z/d²x=[2xcos(x²-2y)]'=2{x'cos(x²-2y)+x[cos(x²-2y)]'}=2[cos(x²-2y)-xsin(x²-2y)2x]=2[cos(x²-2y)-2x²sin(x²-2y)]dz/dy=-2cos(x²-2y)d²z/d²y=[-2cos(x²-2y)]'=-2[cos(x²-2y)]'=-2[-sin(x²-2y)](-2)=-4sin(x²-2y)