x/y=ln(xy)求隐函数y的导数dy/dx,

分类: 作业答案 • 2021-12-19 10:43:59

问题描述：

答

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)]