Question

求方程zsinx＋z²＋xsiny＋xyz＝0所确定的隐函数z的偏导数

Answer 1

问：求方程zsinx＋z²＋xsiny＋xyz＝0所确定的隐函数z的偏导数

答：zsinx+z²+xsiny+xyz=0sinx·∂z/∂x+zcosx+2z∂z/∂x+siny+yz+xy∂z/∂x=0∂z/∂x(sinx+2z+xy)=-zcosx-siny-yz∂z/∂x=-(zcosx+siny+yz)/(sinx+2z+xy)sinx·∂z/∂y+2z∂z/∂y+xcosy+xz+xy∂z/∂y=0∂z/∂y(sinx+2z+xy)=-(xcosy+xz)∂z/∂y=-(xcosy+xz)/(sinx+2z+xy)