求y+x= e∧xy的导数dy⼀dx

2024-11-26 16:53:20
推荐回答(2个)
回答1:

两边对x求导得
dy/dx+1=e^(xy)*(y+x*dy/dx
整理得:[1-x*e^(xy)]*dy/dx=[y*e^(xy)-1]
所以:dy/dx=[y*e^(xy)-1]/[1-x*e^(xy)]

回答2:

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