Question

用导数定义求y=x^(2/3)的导数 注：x的三分之二次方

Answer 1

lim [(x+dx)^(2/3)-x^(2/3)]/dx=lim[(x+dx)^2-x^2]/{[(x+dx)^(4/3)+x^(2/3)*(x+dx)^(2/3)+x^(4/3)]*dx}=lim(2x+dx)/[(x+dx)^(4/3)+x^(2/3)*(x+dx)^(2/3)+x^(4/3)]=2x/[3x^(4/3)]=2/3*x^(-1/3)