=(x2)'arctanx+x2(arctanx)' 2 =2xarctan 2.求下列函数在给定点的导数值， 1)已知f)=snxc0sx,求f"爱 解f'(x)=((sin xcosx) =(sin x)'cosx+sin x(cosx)' (cosx)2-(sin x)2 =cos2x fr月=os2=os号-月 解=写2号r -写25 62可号 o-号吕 @)已知f=1- 1+F 求∫"(4) 四-片授 _0-0+-0-FX1+ +2 =x+网 6
6 ( ) arctan (arctan ) 2 2 = x x + x x 2 2 1 2 arctan x x x x + = + 2. 求下列函数在给定点的导数值. （1） 已知 f (x) = sin x cos x，求 ) 6 ( f . 解 f (x) = (sin x cos x) = (sin x)cos x + sin x(cos x) 2 2 = (cos x) − (sin x) = cos2x 2 1 3 cos 6 ) cos 2 6 ( = = = f (2) 已知 5 5 3 ( ) 2 x x f x + − = ，求 f (2) 解 ) 5 5 3 ( ) ( 2 + − = x x f x ) 5 ) ( 5 3 ( 2 + − = x x x x 5 2 (5 ) 3 2 + − = 15 17 5 4 3 1 f (2) = + = (3) 已知 x x f x + − = 1 1 ( ) ， 求 f (4) . 解 ) 1 1 ( ) ( + − = x x f x 2 (1 ) (1 ) (1 ) (1 )(1 ) x x x x x + − + − − + = 2 (1 ) 1 x + x = −
f0=-i8 1 3.求下列函数的导数 (1)y=sim5x+1) 解y'=sim(5x+1)=cos(5x+1)-(5x+1)y=5cos(5x+1) (2)y=0-x2)1 解y=[1-x2)100y=1001-x2)9.1-x2y=-200.x1-x2)9 (3)y=cosx+e-x y'=(cosx+e)'=(cos)'+(e-)'=-sin ('+e-".(-x)' 2-e (④)y=-snx 解y=(-snxy=0-smxj=1-sm)手.1-snxy COSX 0-m对 (⑤)y=nnx 1 (6)y=arcsin x2 解y=amry-京y-产 (7)y=2sins +tan2x y'=(2tim +tan2x)'=(2sin)+(tan2x)' =2snx In 2.(sin x)'+sec22x.(2x) =2n cosxIn 2+2sec22x (⑧)y=V+x 7
7 18 1 f (4) = − 3. 求下列函数的导数. (1) y = sin( 5x +1) 解 y = [sin( 5x +1)] = cos(5x +1)(5x +1) = 5cos(5x +1) (2) 2 100 y = (1− x ) 解 [(1 ) ] 100(1 ) (1 ) 2 100 2 99 2 y = − x = − x − x 2 99 = −200x(1− x ) (3) x y x e − = cos + 解 = (cos + ) −x y x e = (cos ) + ( ) −x x e = −sin ( ) + (− ) − x x e x x x x e x − = − sin − 2 1 (4) 3 y = 1− sin x 解 ( 1 sin ) [(1 sin ) ] 3 1 3 y = − x = − x (1 sin ) (1 sin ) 3 1 3 2 = − − − x x 3 2 3 (1 sin ) cos x x − = − (5) y = ln ln x 解 (ln ) ln 1 = (ln ln ) = x x y x x ln x 1 = (6) 2 y = arcsin x 解 ( ) 1 1 (arcsin ) 2 4 2 − = = x x y x 4 1 2 x x − = (7) y x x 2 tan 2 sin = + 解 (2 tan 2 ) (2 ) (tan 2 ) sin sin y = + x = + x x x 2 ln 2 (sin ) sec 2 (2 ) sin 2 = x + x x x x x x 2 cos ln 2 2sec 2 sin 2 = + (8) 3 y = 1+ x