大二数学 求详细步骤

大二数学 求详细步骤

(a)
x^3.z^2-5xy^5.z=x^2+y^3
2x^3.z. ∂z/∂x + 3x^2.z - 5y^5.z - 5xy^5. ∂z/∂x = 2x
(2x^3.z -5xy^5).∂z/∂x =2x- 3x^2.z + 5y^5.z
∂z/∂x =(2x- 3x^2.z + 5y^5.z )/(2x^3.z -5xy^5)
----------
x^3.z^2-5xy^5.z=x^2+y^3
2x^3.z.∂z/∂y - 25xy^4.z - 5xy^5. ∂z/∂y = 3y^2
(2x^3.z-5xy^5).∂z/∂y =3y^2 +25xy^4.z
∂z/∂y =(3y^2 +25xy^4.z)/(2x^3.z-5xy^5)
-------
(b)
x^2.sin(2y-5z)=1+ycos(6zx)
2x.sin(2y-5z) + x^2.cos(2y-5z) . (-5∂z/∂x ) = -ysin(6zx) .(6x∂z/∂x +6z)
[6xysin(6zx)-5x^2.cos(2y-5z) ].∂z/∂x = -[6yz.sin(6zx) +2x.sin(2y-5z) ]
∂z/∂x = -[6yz.sin(6zx) +2x.sin(2y-5z) ]/[6xysin(6zx)-5x^2.cos(2y-5z) ]
----------
x^2.sin(2y-5z)=1+ycos(6zx)
x^2.cos(2y-5z) . (2-5∂z/∂y ) =cos(6zx) -ysin(6zx) .(6x.∂z/∂y)
[6xysin(6zx)-5x^2.cos(2y-5z) ]∂z/∂y =cos(6zx) -2x^2.cos(2y-5z)
∂z/∂y =[cos(6zx) -2x^2.cos(2y-5z)]/[6xysin(6zx)-5x^2.cos(2y-5z) ]