由方程y=3x-ln(x+y)+siny所确定隐函数y=y(x)的导数y'

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由方程y=3x-ln(x+y)+siny所确定隐函数y=y(x)的导数y''由方程y=3x-ln(x+y)+siny所确定隐函数y=y(x)的导数y''由方程y=3x-ln(x+y)+siny所确定隐函数

由方程y=3x-ln(x+y)+siny所确定隐函数y=y(x)的导数y'
由方程y=3x-ln(x+y)+siny所确定隐函数y=y(x)的导数y'

由方程y=3x-ln(x+y)+siny所确定隐函数y=y(x)的导数y'
对等式两边求导:y'=3-(1+y')/(x+y)+y'cosy
∴y'=[3(x+y)-1]/[(x+y)(1-cosy)+1]

y'=3-(1+y')/(x+y)+y'cosy,则y'=3(x+y)/(x+y+1+(x+y)cosy)