来自戴余良的问题
【设隐函数y(x)由方程y=sin(x+y)确定,求y"】
设隐函数y(x)由方程y=sin(x+y)确定,求y"
1回答
2020-05-20 23:16
【设隐函数y(x)由方程y=sin(x+y)确定,求y"】
设隐函数y(x)由方程y=sin(x+y)确定,求y"
y'=cos(x+y)(1+y')...(1)
y'=cos(x+y)+cos(x+y)y'
y'=cos(x+y)/[1-cos(x+y)]
对(1)再对x求导,则y''=-sin(x+y)(1+y')(1+y')+cos(x+y)*y''
即[cos(x+y)-1]y''=sin(x+y)(1+y')²
∴【cos(x+y)-1]y''=sin(x+y)/[1-cos(x+y)]²
∴y''=-sin(x+y)/[1-cos(x+y)]³