求由方程X-Y+1/2sinY=1所确定的函数y(x)的二阶导数y··在(1,0)处的值~\(≧▽≦)/~
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![求由方程X-Y+1/2sinY=1所确定的函数y(x)的二阶导数y··在(1,0)处的值~\(≧▽≦)/~](/uploads/image/z/5410593-9-3.jpg?t=%E6%B1%82%E7%94%B1%E6%96%B9%E7%A8%8BX-Y%2B1%2F2sinY%3D1%E6%89%80%E7%A1%AE%E5%AE%9A%E7%9A%84%E5%87%BD%E6%95%B0y%28x%29%E7%9A%84%E4%BA%8C%E9%98%B6%E5%AF%BC%E6%95%B0y%C2%B7%C2%B7%E5%9C%A8%281%2C0%29%E5%A4%84%E7%9A%84%E5%80%BC%7E%5C%28%E2%89%A7%E2%96%BD%E2%89%A6%29%2F%7E)
求由方程X-Y+1/2sinY=1所确定的函数y(x)的二阶导数y··在(1,0)处的值~\(≧▽≦)/~
求由方程X-Y+1/2sinY=1所确定的函数y(x)的二阶导数y··在(1,0)处的值~\(≧▽≦)/~
求由方程X-Y+1/2sinY=1所确定的函数y(x)的二阶导数y··在(1,0)处的值~\(≧▽≦)/~
对x求导得到
1-y' +0.5cosy *y'=0
所以
y'=1/(1-0.5cosy)
而继续求导得到
y"= -1/(1-0.5cosy)^2 * (0.5siny) *y'
再代入y'
即
y"= -1/(1-0.5cosy)^3 * (0.5siny)
代入x=1,y=0,
显然得到
y"= 0