Question

求函数的偏导数

求函数Z=f(x,xy)的偏导数

Answer 1

z = f(x, xy), 令 u = x， v = xy， 则
∂z/∂x = (∂f/∂u)(∂u/∂x) + (∂f/∂v)(∂v/∂x) = ∂f/∂u + y(∂f/∂v)
∂z/∂y = (∂f/∂u)(∂u/∂y) + (∂f/∂v)(∂v/∂y) = x(∂f/∂v)