用导数的定义求函数y=根号下（x-1）的导数

y=(x-1)½,任给自变量的增量⊿x,⊿y=f(x+⊿x)-f(x)=(⊿x+x-1)½-(x-1)½=[(⊿x+x-1)½]²-[(x-1)½]²/[(⊿x+x-1)½+(x-1)½]=⊿x/[(⊿x+x-1)½+(x-1)½],⊿y/⊿x.=1/2（x-1)^(-1/2),所以lim⊿y/⊿x=lim1/2(x-1)^(-1/2)(⊿x→0).所以y=根号下（x-1)的导数是1/2(x-1)^(-1/2)