Question

y=x^3+xe^y求dy

个人觉得应该是多元函数求导，请高手详细写一下过程，感激不尽

Answer 1

y=x^3+xe^y
d(y)=d(x^3+xe^y)
dy=d(x^3)+d(xe^y)
dy=3x^2dx+e^ydx+xd(e^y)
dy=3x^2dx+e^ydx+xe^ydy
dy=(3x^2+e^y)dx/(1-xe^y)

Answer 2

dy=3x²dx+e^y*dx+x*e^y*dy
(1-x*e^y)dy=(3x²+e^y)dx
dy/dx=(3x²+e^y)/(1-x*e^y)