例2设函数f)=sinx,求sinx)及( sin x)'T=g 解: sin x)= lim sIn(x+△x)-six △x→>0 △ Ar0 cos(+t Sin 4 r 2′△x -coSX 即(sinx)y=cosx (sInx I==cos划、=兀 2 同理可求(cosx sinr例2 设函数f(x)=sinx,求(sinx)及 4 (sin )  =  x x 解: x x x x x x  +  −  =  → sin( ) sin (sin ) lim 0 x x x x x    = +  → 2 sin ) 2 lim 2cos( 0 =cosx 即(sinx)=cosx 4 4 (sin )  cos  = =   = x x x x 2 2 = 同理可求(cosx)= −sinx