f为可微函数,z=f(x+y+z,xyz),z对x求导得多少,怎么求?
问题描述：
f为可微函数,z=f(x+y+z,xyz),z对x求导得多少,怎么求?
答
为了书写简单,这样记：x+y+z=u xyz=v ez/ex=m【e是指偏导的意思】ez/ex=ef/eu*eu/ex+ef/ev*ev/ex=ef/eu*(1+ez/ex)+ef/ev*(yz+xyez/ex)即：m=ef/eu*(1+m)+ef/ev*(yz+xym)m(1-ef/eu-xy*ef/ev)=ef/eu+yz*ef/evm=【ef/eu...