设函数z由xcosy+ycosz+zcosx=1所确定,则全微分dz=?
问题描述：
设函数z由xcosy+ycosz+zcosx=1所确定,则全微分dz=?
答
等式两边对x求偏导：cosy-ysinz* Z'x+Z'x* cosx-zsinx=0, 得：Z'x=(zsinx-cosy)/(cosx-ysinz)
等式两边对y求偏导：-xsiny+cosz-ysinz*Z'y+Z'y*cosx=0,得：Z'y=(xsiny-cosz)/(cosx-ysinz)
因此dz=Z'x*dx+Z'y*dy=[(zsinx-cosy)dx+(xsiny-cosz)dy]/(cosx-ysinz)