2.求导数举例步骤：(1)求增量Ay = f(x +Ax)- f(x);Ay -f(x+Ax)- f(x)(2)算比值AxAxAy(3)求极限y'= limAr-→0 △x例1 求函数 f(x)=C(C为常数)的导数,f(x+h)- f(x)C-C解 f'(x)=lim：0.limhhh-→>0h-→0即(C)' = 0.微积分经济数学
2. 求导数举例 步骤: (1)求增量 y = f (x + x) − f (x);; ( ) ( ) (2) x f x x f x x y + − = 算比值 (3) lim . 0 x y y x = → 求极限 例1 求函数 f (x) = C(C为常数)的导数. 解 h f x h f x f x h ( ) ( ) ( ) lim 0 + − = → h C C h − = →0 lim = 0. 即 (C) = 0
例2设函数 f(x) = sin x,求(sin x)及(sin x)元4sin(x + h)- sin x解(sin x)'= limhh-→0hsinh2= lim cos(x +cos x.h2h-→02即(sin x)' = cos x./2(sin x=cosx元元244经济数学微积分
例 2 ( ) sin , (sin ) (sin ) . 4 = = x 设函数 f x x 求 x 及 x 解 h x h x x h sin( ) sin (sin ) lim0 + − = → 2 2 sin ) 2 lim cos( 0 h h h x h = + → = cos x . 即 (sin x) = cos x. 4 4 (sin ) cos = = = x x x x . 22 =