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z等于F(sin2x.x^2y)求xy混合二阶偏导数

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/...

z=e^2xsin(x+2y) dz=2e^2xsin(x+2y)dx+e^2xcos(x+2y)(dx+2dy) =[2e^2xsin(x+2y)+e^2xcos(x+2y)]dx+2e^2xcos(x+2y)dy 所以: z对x的偏导数=2e^2xsin(x+2y)+e^2xcos(x+2y)=e^2x[2sin(x+2y+cos(x+2y)] z对y的偏导数=2e^2xcos(x+2y).

u=√(sin²x+sin²y+sin²z) 那么u 对z 求偏导数 得到 u'z= 1/ 2√(sin²x+sin²y+sin²z) *(sin²z)' =1/ 2√(sin²x+sin²y+sin²z) * 2sinz *cosz =sinz *cosz / √(sin²x+sin²y+sin²z)

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