来自聂时贵的问题
e的(xy)次方+tan(xy)=y,求y‘(0)
e的(xy)次方+tan(xy)=y,求y‘(0)
1回答
2020-08-02 08:40
e的(xy)次方+tan(xy)=y,求y‘(0)
e的(xy)次方+tan(xy)=y,求y‘(0)
x=0
则e^0+tan0=y
y=1
对x求导
e^(xy)*(y+x*y')+sec²(xy)*(y+x*y')=y'
[e^(xy)+sec²(xy)]*y+[e^(xy)+sec²(xy)]*x*y'=y'
y'=[e^(xy)+sec²(xy)]/1-xe^(xy)-xsec²(xy)]
所以y'(0)=(1+1)/[1-0-0]=2