例2设函数∫(x)=sinx,求sinx)及sinx)yx 1 Ff f(r)=lim ff(x+h)-f(x) h→>0 lim sin(x +h)-sinx 2cos(x+)·sin lim h→>0 h h SIn lim cos(x+。)2 h→>0 h=cos x 2 (sin x)=cos x. ∴(sinx)x= cosx 2 Economic-mathematics 31-4 Wednesday, February 24 2021Economic-mathematics 31 - 4 Wednesday, February 24, 2021 例2 ( ) sin , (sin ) (sin ) . 4  = =   x 设函数 f x x 求 x 及 x 解 h x h x h sin( ) sin lim 0 + − = → 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 . 2 2 = h f x h f x f x h ( ) ( ) ( ) lim 0 + −  = → h h h x h 2 ) sin 2 2cos( lim 0 +  =  →