求由方程x^4-xy+y^4=xsiny所确定的隐函数的导数d^2y/dx^2在(0,0)处的值

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求由方程x^4-xy+y^4=xsiny所确定的隐函数的导数d^2y/dx^2在(0,0)处的值

求由方程x^4-xy+y^4=xsiny所确定的隐函数的导数d^2y/dx^2在(0,0)处的值
求由方程x^4-xy+y^4=xsiny所确定的隐函数的导数d^2y/dx^2在(0,0)处的值

求由方程x^4-xy+y^4=xsiny所确定的隐函数的导数d^2y/dx^2在(0,0)处的值

红色圈出

两边求导得
4x^3-y-xy'+4y^3y'=siny+xcosy*y'
x=0,y=0代入得
没法求出来y'
两边再求导得
12x^2-y'-y'-xy''+12y^2(y')^2+4y^3y''=cosy*y'+cosy*y'-xsiny*(y')^2+xcosy*y''