求z=f(y/x,x^2y)的所有二阶偏导数，要详细步骤，有详细步骤才给分，万分感谢

Answer 1

对
z = f(y/x,x²y),
分别对 x,y 求偏导数,有
Dz/Dx = f1*(-y/x²)+f2*(2xy) = -(y/x²)f1+2xyf2,
Dz/Dy = f1*(1/x)+f2*x² = (1/x)f1+x²f2,
进而
D²z/Dx² = (D/Dx)[-(y/x²)f1+2xyf2]
= -(-2y/x³)f1-(y/x²)[f11*(-y/x²)+f12*(2xy)]+2yf2+2xy[f21*(-y/x²)+f22*(2xy)]
= ……,
……（类似,留给你）

追问

我都说了要详细步骤
从别人那儿复制粘贴一下是几个意思？