u=(e^x)/y
∂u/∂x = (e^x)/y ∂u/∂y = -(e^x)/y^2
du = (∂u/∂x)dx + (∂u/∂y)dy = [(e^x)/y]dx - (1/y^2)dy
v = z/xy
∂x/∂x = -zy/x^2 ∂v/∂y = -zx/y^2 ∂v/∂z = 1/xy
dv = (-zy/x^2)dx + (-zx/y^2)dy + (1/xy)dz
dw=(∂f/∂u)du + (∂f/∂v)dv
比如 w=f(u,v)=u^2 + v^3
dw = 2udu + 3v^3dv
将u,v和上面求得的du和dv代入计算就可以得到结果了.