链式法则如图示 az az au az av,2 ax au ax ay ax L azaz au az a ay au ay av a 例设z=e"simv,而n=,=x+y,求和bz ax ay 解 + ,<,型 =e"sinv:y+e"cosp·1 e lysin(x+y)+ cos( +y) azaz au az av ay au ay av a =e"sinv·x+e"cosv·1 elrsin(x+ y)+cos(x y)7 链式法则如图示 z x ∂ = ∂ ⋅ ∂ ∂ u z x u ∂ ∂ ⋅ ∂ ∂ + v z x v ∂ ∂ z y ∂ = ∂ ⋅ ∂ ∂ u z y u ∂ ∂ ⋅ ∂ ∂ + v z y v ∂ ∂ u v x z y u v x z y 解 z x ∂ = ∂ ⋅ ∂ ∂ u z x u ∂ ∂ ⋅ ∂ ∂ + v z x v ∂ ∂ = e sinv ⋅ y + e cos v ⋅1 u u z y ∂ = ∂ ⋅ ∂ ∂ u z y u ∂ ∂ ⋅ ∂ ∂ + v z y v ∂ ∂ = e sin v ⋅ x + e cos v ⋅ 1 u u z u v x y 型 e [ y sin( x y) cos(x y)] xy = + + + e [x sin( x y) cos(x y)] xy = + + + y z x z z e v u xy v x y u ∂ ∂ ∂ ∂ 例 设 = sin ，而 = ， = + ，求 和