Question

隐函数dy/dxxe^y+ye^x=0

Answer 1

xe^y+ye^x=0

对x求导

x'*e^y+x*(e^y)'+y'*e^x+y*(e^x)'=0

e^y+x*e^y*y'+y'*e^x+y*e^x=0

(e^y+ye^x)+(xe^y+e^x)*y'=0

y'=-(e^y+ye^x)/(xe^y+e^x)

所以dy/dx=-(e^y+ye^x)/(xe^y+e^x)