求由e^(x+y)+sin(xy)=x确定的隐函数y=f(x)导数或微分

2025-02-27 16:43:14
推荐回答(4个)
回答1:

对x求导有:
e^(x+y)*(1+y')+cos(xy)(y+xy')=1
[e^(x+y)+cos(xy)x]y'=1-e^(x+y)-y*cos(xy)
y'=[1-e^(x+y)-y*cos(xy)] / [e^(x+y)+cos(xy)x]

回答2:

回答3:

e^(x+y)+sin(xy)=x

(1+y')e^(x+y)+[cos(xy)](y+xy')=1

y'=-[e^(x+y)+ycos(xy)-1]/[e^(x+y)+xcos(xy)]

回答4:

两边关于x求导