像这类隐函数的题,最好先求导数,然后再写为dy = dx的形式.
两边对x求导:
y' = e^y + x(e^y)y'
(1 - xe^y)y' = e^y
y' = (e^y)/(1 - xe^y)
dy = (e^y)dx/(1 - xe^y)
高数微分问题已知y=1+xe^y,求dy.两边去微分：dy=d(1+xe^y)=e^ydx+xe^ydy为什么后面是dy
像这类隐函数的题,最好先求导数,然后再写为dy = dx的形式.
两边对x求导:
y' = e^y + x(e^y)y'
(1 - xe^y)y' = e^y
y' = (e^y)/(1 - xe^y)
dy = (e^y)dx/(1 - xe^y)