u=x+y =>∂u/∂x=1, ∂u/∂y=1
v=x-y =>∂v/∂x=1, ∂v/∂y=-1
z=u^2+v^2+uv
∂z/∂x
=2u. ∂u/∂x + 2v.∂v/∂x + u.∂v/∂x + v.∂u/∂x
=2(x+y)(1) +2(x-y)(1) + (x+y).(1) + (x+y)(1)
=3(x+y) +3(x-y)
=6x
∂z/∂y
=2u. ∂u/∂y + 2v.∂v/∂y + u.∂v/∂y + v.∂u/∂y
=2(x+y)(1) +2(x-y)(-1) + (x+y).(-1) + (x+y)(1)
=3(x+y) -3(x-y)
=6y
内容全部来源于网络收集，如有侵权，请联系网站删除：QQ：24596024