高等数学 微分方程 求步骤,,在线等 秒加分

2025-05-10 03:13:18
推荐回答(1个)
回答1:

令 u = cos(x^2+y^2), v= xy
∂z/∂x = (∂f/∂u)(∂u/∂x)+ (∂f/∂v)(∂v/∂x) = -2xsin(x^2+y^2) (∂f/∂u)+y∂f/∂v
∂z/∂y = (∂f/∂u)(∂u/∂y)+ (∂f/∂v)(∂v/∂y) = -2ysin(x^2+y^2) (∂f/∂u)+x∂f/∂v
dz = (∂z/∂x)dx + (∂z/∂y)dy
= [ -2xsin(x^2+y^2) (∂f/∂u)+y∂f/∂v]dx + [-2ysin(x^2+y^2) (∂f/∂u)+x∂f/∂v]dy