来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/08/26 02:40:43
求隐函数的“二阶导数”.
![](http://img.wesiedu.com/upload/3/9d/39d09b0428ba42bca18be9b6ad15e262.jpg)
两边对x求导:2b^2x+2a^2yy'=0,得:y'=-(b^2/a^2)*(x/y)
将y'对x再求导:y"=-(b^2/a^2)* (y-xy')/y^2
代入y'得:y"=-(b^2/a^2)*(y+b^2/a^2*x^2/y)/y^2
=-(b^2/a^2)*(a^2y^2+b^2x^2)/(a^2y^3)
=-(b^2/a^2)*a^2b^2/(a^2y^3)
=-b^4/(a^2y^3)