Question

设方程e^y+xy=e确定了函数y=y(x),求y'|x=0

Answer 1

e^y+xy=e

对x求导

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

(e^y+x)y'=-y

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

当x=0时,y=1

y'=-1/(e+0)=-1/e