例3求函数y=x"(m为正整数的导数 解f(x)=lim f∫(x+h)-f(x) (x+h)"-x h→>0 h→0 h =mh-1,n(n-1) h→0 2!x"h+…+h"-1 即(x") 更一般地(x)=x-1.(∈R) 例如,(x)y=(x2)=1x (x-)=(-1)x Economic-mathematics 31-5 Wednesday, February 24 2021Economic-mathematics 31 - 5 Wednesday, February 24, 2021 例3 求函数 y x (n为正整数)的导数. n = 解 h x h x n n h + − = → ( ) lim 0 ] 2! ( 1) lim[ 1 2 1 0 − − − → + + − = + n n n h x h h n n nx  −1 = n nx ( ) . −1  = n n 即 x nx 更一般地 ( ) . ( ) 1 x  = x  R −     ( ) ( ) 2 1 例如, x  = x  1 2 1 2 1 − = x . 2 1 x = ) ( ) 1 ( 1  =  − x x 1 1 ( 1) − − = − x . 1 2 x = − h f x h f x f x h ( ) ( ) ( ) lim 0 + −  = →