Question

设y=x乘以e的y+1次方,则dy/dx=?请写清楚过程,

Answer 1

y=xe^(y+1)

dy=e^(y+1)dx+xde^(y+1)

dy=e^(y+1)dx+xe^(y+1)d(y+1)

dy=e^(y+1)dx+xe^(y+1)dy

[1-xe^(y+1)]dy=e^(y+1)dx

dy/dx=e^(y+1)/[1-xe^(y+1)]