Question

求函数z=sin2/x-x3y2+2的二阶偏导数

Answer 1

问：求函数z=sin2/x-x3y2+2的二阶偏导数

答：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)