求隐函数的“二阶导数”.
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求隐函数的“二阶导数”.
![](http://img.wesiedu.com/upload/3/9d/39d09b0428ba42bca18be9b6ad15e262.jpg)
![](http://img.wesiedu.com/upload/3/9d/39d09b0428ba42bca18be9b6ad15e262.jpg)
![求隐函数的“二阶导数”.](/uploads/image/z/18945109-37-9.jpg?t=%E6%B1%82%E9%9A%90%E5%87%BD%E6%95%B0%E7%9A%84%E2%80%9C%E4%BA%8C%E9%98%B6%E5%AF%BC%E6%95%B0%E2%80%9D.)
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)
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)