求由方程y的5次方+2y-x-3x7次方=0所确定的隐函数y=y(x)的导数dy/dx和dy/dx│x=0
问题描述:
求由方程y的5次方+2y-x-3x7次方=0所确定的隐函数y=y(x)的导数dy/dx和dy/dx│x=0
答
两边对x求导得
5y^4y'+2y'-1-3x^6=0
整理得y'=dy/dx=(3x^6+1)/(5y^4+2)
令x=0 则y=0
从而dy/dx│x=0 = 0.5