由方程cos(x+y)+e^y=x确定y和x的隐函数,求dy

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/08 06:09:52
由方程cos(x+y)+e^y=x确定y和x的隐函数,求dy

由方程cos(x+y)+e^y=x确定y和x的隐函数,求dy
由方程cos(x+y)+e^y=x确定y和x的隐函数,求dy

由方程cos(x+y)+e^y=x确定y和x的隐函数,求dy
两边求导,-sin(x+y)(1+y`)+e^yy`=1,dy=1+sin(y+x)/e^y-sin(x+y)dx

两边同对x求导-(1+y')sin(x+y)+y'e^y=1…我不会。。

两边对求导:
-[sin(x + y)]*(x + y)' + (e^y)*y' = 1
-[sin(x + y)]*(1 + y') + (e^y)*y' = 1
[e^y - sin(x + y)]y' = 1 + sin(x + y)
y' = [1 + sin(x + y)]/[e^y - sin(x + y)]
dy = [1 + sin(x + y)]dx/[e^y - sin(x + y)]