Question

求Y=1+xe^y的微分麻烦给一下过程,越详细越好,谢谢

Answer 1

y=1+xe^y ==>y'=(1+xe^y )'

==>y'=(xe^y)'

==>y'=1*e^y+xe^y*y'

==>y'(1-xe^y)=e^y

==>y'=e^y/(1-xe^y)

因为y=1+xe^y,则1-xe^y=2-y,得y'=e^y/(2-y)

即dy/dx=e^y/(2-y)

dy=[e^y/(2-y)]dx