设u=xy,v=y/x,则z=x³f(u,v),au/ax=y,av/ax=-y/x²
故az/ax=3x²f(u,v)+x³f'u(u,v)(au/ax)+x³f'v(u,v)(av/ax)
=3x²f(u,v)+x³yf'u(u,v)-xyf'v(u,v)
(f'u(u,v)表示f(u,v)关于u的偏导数,f'v(u,v)表示f(u,v)关于v的偏导数)