函数z=f(x,y)由方程2sin(2x+3y-2z)=1x+1y+1z所确定求z的所有二阶偏导数.docx

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1、函数z=f(x,y)由方程2in(2x+3y-2z)=1x+1y+1z所确定，求z的所有二阶偏导数。主要内容：222通过全微分法求出一阶偏导数法，再求出三个二阶偏导数等、号和当OSySXay一、全微分求出一阶偏导数：*.*2sin(2x+3y-2z)=1x+1y+1z,2cos(2x+3y-2z)*(2dx+3dy-2dz)=1x+1y+1z,化简得：4cos(2x+3y-2z)-1dx+2cos(2x+3y-2z)-1dy=1+4cos(2x+3y-2z)dz,即：z4cos(2x+3y-2z)-1z2cos(2x+3y-2z)-11+4cos(2x+3y-2z)Hy1+4cos(2x+3y

2、-2z)二、求三个二阶偏导数(1)对雪,直接通过函数商的求导法则计算Z对X的二阶偏导数号o2-4sin(2x+3y-2z)(22-)1+4cos(2x+3y-2z)+44cos(2x+3y-2z)-1sin(2x+3y-2z)(2-2-)ZX1+4cos(2x+3y-2z)22z/cAaZ、.小CC,44cos(2x+3y-2z)-1-41+4cos(2x+3y-2z)皮=(2-W)s(23y-2z)1+4cos(2x3y-2z)2，(2)先对一阶偏导数詈进行变形，再求出二阶偏导数学,步骤如下：.z2cos(2x+3y-2z)T_W1y1+4cos(2x3y-2z)22,4cos(2x+3y-2z)+1kz3-4sin(2x+3y-2z)(3-2)i4cos(2x+3y-2z)+12即：zsin(2x+3y-2z)(3-2靠)二_2in(2x+3y-2z)y74cos(2x+3y-2z)+174cos(2x+3y-2z)+1:(3)由对X再次求偏导数，计算混合二阶偏导数，计算步骤如下:,2.2o4sin(2x+3y-2z)(2-2)dZdzJ0Xyy24cos(2x+3y-2z)+12a2zSMZ+3y2)(2-旗)二_222si(2x+3y-2Z)y4cos(2x+3y-2z)+124cos(2x+3y-2z)+1j