xy=e^x+y 确定隐函数y的导数dy/dx

来源:学生作业帮助网 编辑:作业帮 时间:2024/11/08 15:34:23

xy=e^x+y 确定隐函数y的导数dy/dx
xy=e^x+y 确定隐函数y的导数dy/dx

xy=e^x+y 确定隐函数y的导数dy/dx
xy = e^x +y
xy' + y = e^x + y'
y'(1-x) = y -e^x
y' = (y-e^x)/(1-x)

xe^x+1-x

∵xy=e^(x+y)
∴d(xy)=d[e^(x+y)]
∴y+xdy/dx=d(x+y)e^(x+y)=(1+dy/dx)e^(x+y)
∴(x-e(x+y))dy/dx=e^(x+y)-y
∴dy/dx=[e^(x+y)-y] / [x-e(x+y)]