问题补充:
设函数z=f(sinx,xy),其中 具有二阶连续偏导数,求ε^2z/εxεy
答案:
设u=sinx,v=xy
dz/dx=dz/du*du/dx+dz/dv*dv/dx=cosxf1+yf2
d^2z/dxdy=d(dz/dx)/dy=(-sinx)f1+cosx*df1/dx+y*df2/dx
=-sinxf1+cosx(df1/du*du/dx+df1/dv*dv/dx)+y(df2/du*du/dx+df2/dv*dv/dx)
=-sinxf1+cosx(cosxf11\+yf12\)+y(cosxf21\+yf22\)
=-sinxf1+(cosx)^2f11\+(y+ycosx)f12\+y^2f22\
f1,f11\,f12\,f22\分别指df/du,d^2f/du^2,d^2f/dudv,d^2f/dv^2