2x^3 + 3y^3 = 5,求y''
问题描述：
2x^3 + 3y^3 = 5,求y''
求二次导,谢谢!
答
2x^3 + 3y^3 = 5两边同时对x求导,得6x^2+9y^2·y'=0y'=-2x^2/3y^2y''=-(4x·3y^2-2x^2·6y·y')/9y^4=-(12xy^2-12x^2y·(-2x^2/3y^2))/9y^4=-(12xy^2+(8x^4/y))/9y^4=-(12xy^3+8x^4)/9y^5