)22+0女 a cos x sIn a2+1 2unv.-+-3 n(3x-2y)+ 2(3x-2 azaz a 2ulnv(-2)+-(-2) 2x2 2x2 n(3x-2y)- y2(3x-2 (5)如=amha a or d ar u2x +u. 22.ycosx r(2x+2y sin x cos x) au au du az l·2y+l·2-·2 sinx (2y+4y sin2x) 记=x-+y-+2-,=x+γ+2。 则 aw ax a ay aw az as Cx as ay as a- as x(sin u+ 2xv cos u)+o(sin u+ 2yv u)+=(sin u+ 2=v cos u) te(sin u+ 2xvcosu)+e(sin u+2-v cos u) e(sin u+2xv cos u)+y(sin u+2 yv cos u)+=(sin u+2=v cos u) e(sin u+ 2xvcosu)+e(sin u+ 2yv cosu)+e(sin u+ 2= u)(3) dw w w dy w dz dx x y dx z dx ∂ ∂ ∂ = + + ∂ ∂ ∂ 2 2 2 ( ) cos ( sin ) 1 1 1 ax ax ax ae y z e e a x x a a a − = + ⋅ − ⋅ − + + + sin ax = e x。 (4) dz z u z dv dx u x v dx ∂ ∂ ∂ = + ∂ ∂ ∂ 2 1 2 ln 3 u u v y v = ⋅ + ⋅ 2 2 2 2 3 ln(3 2 ) (3 2 ) x x x y y y = − + x − y ， z z u z v y ∂ y u y v ∂ ∂ ∂ ∂ ∂ = + ∂ ∂ ∂ ∂ 2 2 2 ln ( ) ( 2) x u u v y v = ⋅ − + ⋅ − 2 2 3 2 2 2 ln(3 2 ) (3 2 ) x x x y y y = − − − x − y 。 (5) u u du z x x dz ∂ ∂ = + ∂ ∂ x x ∂ ∂ 2 = ⋅ u x2 2 + u z ⋅ ⋅ y cos x 224 2 sin 4 (2 2 sin cos ) x y y x e x y x + + = + u u du z y y dz y ∂ ∂ ∂ = + ∂ ∂ ∂ = ⋅ u y 2 2 + u ⋅ z⋅ 2y sin x 224 2 sin 3 2 (2 4 sin ) x y y x e y y + + = + x 。 (6) 记u = x 2 + y 2 + z 2，v = x + y + z 。则 w w x w y w s x s y s z ∂ ∂ ∂ ∂ ∂ ∂ ∂ = + + ∂ ∂ ∂ ∂ ∂ ∂ ∂ z s = x(sin u + 2xv u cos ) + + 0(sin u 2yv u cos ) + + z(sin u 2zv cosu) (sin 2 cos ) (sin 2 cos ) s s t te u xv u e u zv u + = + + + w w x w y w t x t y t z ∂ ∂ ∂ ∂ ∂ ∂ ∂ = + + ∂ ∂ ∂ ∂ ∂ ∂ ∂ z t (sin 2 cos ) (sin 2 cos ) (sin 2 cos ) s = + e u xv u + y u + yv u + z u + zv u (sin 2 cos ) (sin 2 cos ) (sin 2 cos ) s t s t e u xv u e u yv u e u zv u + = + + + + + 。 2