Question

设方程e^y+xy=1确定隐函数y=y(x),则y'(0)=?

Answer 1

y'(0)意思是先求出y',然后再代入x=0 用 y=f(x)来说明 y'(0)意为先求出f'(x).令x=0则得f'(0)

e^y+xy=1 则 e^y=1-xy 两边对x求导

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

则 y'=y/(e^y-x);

当x=0时.代入e^y+xy=1 求出y=0

则y'(0)=y/(e^y-x)｜(x=0)

=0/(1-0)

=0