(p=+. 国x+_M (3) ] 因= M东+为小-xx+ 红+xh -lim -M)x)--x)] x+x许 M红+包x红+国 h x+kiMx) Mxhx)-uxW) 法则(3)可简单地表示为 （恤=.(mer4,肖=r 12 定理1中的法则()2)可推广到任意有限个可导函数的情形.例如，设以、=州 =(x)均可导，则有 (叶-'=W+-. (awy=[(uv)wl'=mYw+(w)w' Wv+wr'hr+iw=ww+N'w+inw. 即 (wY■1w+w+w/, 在法则2)中.如果=CC为常数).则有 (C'=C. 例1.5=2x3-5x2+3x-7.求y 解：y/=(2x-5x2+3w-7'=(2xy-5x2y+3-=2x2y-5x2y+3新xy -23r3-52r+3-6r2-10r+3 例2-+4e-m受，求f国及八受 解：-(y44eof-(sny-32-4snx, 八-4 例3.='(sin+e0s,求y 解：y'=(e'Y(s1nx+eos+e(sn+cos ry e'(sin xtcos x)te'(cos x-sin x) -2e'0o6L 例4.=anx,求 解：/=(an=(sn=snx)cosx--sin.x(cosr) COST COBI =90ex+sn2x。1 co=sed. 即 ('-立， 制5.=c工，求 (uv)=uv+uv (3) v x h v x h u x h v x u x v x h h v x u x v x h u x h v x u x h h ( ) ( ) ( ) ( ) ( ) ( ) lim ( ) ( ) ( ) ( ) lim ( ) ( ) 0 0 + + − + = − + + =        → → v x h v x h u x h u x v x u x v x h v x h ( ) ( ) [ ( ) ( )] ( ) ( )[ ( ) ( )] lim 0 + + − − + − = → ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) lim 0 v x h v x h v x h v x v x u x h u x h u x h + + − − + − = → ( ) ( ) ( ) ( ) ( ) 2 v x u  x v x −u x v  x =  法则(3)可简单地表示为 2 ( ) v u v uv v u  −   =  (uv)=uv (uv)=uv+uv 2 ( ) v u v uv v u  −   =  定理 1 中的法则(1)、(2)可推广到任意有限个可导函数的情形 例如 设 u=u(x)、v=v(x)、 w=w(x)均可导 则有 (u+v−w)=u+v−w (uvw)=[(uv)w]=(uv)w+(uv)w =(uv+uv)w+uvw=uvw+uvw+uvw 即 (uvw) =uvw+uvw+uvw 在法则(2)中 如果 v=C(C 为常数) 则有 (Cu)=Cu 例 1．y=2x 3−5x 2+3x−7 求 y 解 y=(2x 3−5x 2+3x−7)= (2x 3 )−(5x 2 )+(3x)−(7)= 2 (x 3 )− 5( x 2 )+ 3( x) =23x 2−52x+3=6x 2−10x+3 例 2 2 ( ) 3 4cos sin  f x =x + x−  求 f (x)及 ) 2 (  f   解 f x x x ) 3x 4sin x 2 ( )=( 3)+(4cos )−(sin  = 2 −   4 4 3 ) 2 ( = 2 −  f  例 3．y=e x (sin x+cos x) 求 y 解 y=(e x )(sin x+cos x)+ e x (sin x+cos x) = e x (sin x+cos x)+ e x (cos x −sin x) =2e x cos x 例 4．y=tan x  求 y 解 x x x x x x x y x 2 cos (sin ) cos sin (cos ) ) cos sin (tan ) (  −   =  =  = x x x x x 2 2 2 2 2 sec cos 1 cos cos sin = = + =  即 (tan x)=sec2 x  例 5．y=sec x 求 y