设Z=f(x^2 +y,2xy),求dz/dx和dz/dy

题目

设Z=f(x^2 +y,2xy),求dz/dx和dz/dy

答案

u = x^2 + y∂u/∂x = 2x ∂u/∂y = 1du = (∂u/∂x)dx + (∂u/∂y)dy = 2xdx + dyv = 2xy∂v/∂x = 2y ∂v/∂y = 2xdv = (∂v/∂x)dx + (&...