作业帮高等数学偏导数问题
来源：学生作业帮 编辑：拍题作业网作业帮 分类：数学作业 时间：2024/04/28 02:31:07
高等数学偏导数问题
对方程两边求微分,得
dz = f1*(ydx+xdy)+f2*[e^(xy)](ydx+xdy)
= y{f1+[e^(xy)]*f2}dx+x{f1+[e^(xy)]*f2}dy
可得
Dz/Dx = y{f1+[e^(xy)]*f2},Dz/Dy = x{f1+[e^(xy)]*f2}.
于是
D²z/Dx² = (D/Dx)[y{f1+[e^(xy)]*f2}]
= y{(D/Dx)f1+(D/Dx)[e^(xy)]*f2+[e^(xy)]*(D/Dx)f2}
= y{y{f11+[e^(xy)]*f12}+y[e^(xy)]*f2+[e^(xy)]*y{f21+[e^(xy)]*f22}}
= …….
dz = f1*(ydx+xdy)+f2*[e^(xy)](ydx+xdy)
= y{f1+[e^(xy)]*f2}dx+x{f1+[e^(xy)]*f2}dy
可得
Dz/Dx = y{f1+[e^(xy)]*f2},Dz/Dy = x{f1+[e^(xy)]*f2}.
于是
D²z/Dx² = (D/Dx)[y{f1+[e^(xy)]*f2}]
= y{(D/Dx)f1+(D/Dx)[e^(xy)]*f2+[e^(xy)]*(D/Dx)f2}
= y{y{f11+[e^(xy)]*f12}+y[e^(xy)]*f2+[e^(xy)]*y{f21+[e^(xy)]*f22}}
= …….