x/y=ln(xy)求隐函数y的导数dy/dx,

来源:学生作业帮助网 编辑:六六作业网 时间:2024/11/24 20:45:29
x/y=ln(xy)求隐函数y的导数dy/dx,x/y=ln(xy)求隐函数y的导数dy/dx,x/y=ln(xy)求隐函数y的导数dy/dx,x=yln(xy),等式两端对x求导,1=dy/dx+y

x/y=ln(xy)求隐函数y的导数dy/dx,
x/y=ln(xy)求隐函数y的导数dy/dx,

x/y=ln(xy)求隐函数y的导数dy/dx,
x=yln(xy),等式两端对x求导,1=dy/dx+y[1/ln(xy)][y+x(dy/dx)]=dy/dx+y/ln(xy)+xdy/dx,整理得
(dy/dx)(1+x)=1-y/ln(xy),即dy/dx={[ln(xy)-y]/[(1+x)ln(xy)]