导数练习题(含答案)
【编著】黄勇权
一、求下函数的导数
(1)f (x )=2x 2+3x+2 (2)f (x )=3sinx+7x 2 (3)f (x )=lnx+2x
(4)f (x )=2x +6x (5)f (x )=4cosx -7 (6)f (x )=7e x +9x
(7)f (x )=x 3+4x 2+6 (8)f (x )=2sinx -4cosx (9)f (x )=log2x
(10)f (x )=
x
1 (11)f (x )=lnx+3e x (12)f (x )=2x x
(13)f (x )=sinx 2 (14)f (x )=ln (2x 2+6x )
(15)f (x )=x 1x 3x 2++ (16)f (x )=xlnx+9x
(17)f (x )=
x
sinx lnx + (18)f (x )=tanx
(19)f (x )=x x
e 1e 1-+ (20)
f (x )=(x 2-x )3
【答案】
一、求下函数的导数
(1)f /=4x+3 (2)f /=3cos+14x (3)f /=x
1+2 (4)f /=2x ln2+6 (5)f /= -4sinx (6)f /=7e x
(7)f /=3x 2+8x (8)f /=2cosx+4sinx
(9)因为f (x )=log2x =2ln lnx =lnx 2
ln 1?
所以:f /=(lnx 2ln 1?)/ =(2ln 1)?(lnx )/ =2ln 1?x 1 =ln2
x 1?
(10)因为:f (x )=x
1 f /=2x x 1x 1)
()()('?-?'= x x 1210?- = x x 21- = 2x 2x -
(11)f /=
x e 3x 1+
(12)f (x )=
2x x =23x - f /=(2
3-)25x -= 3
x 2x 3- (13)f /=(sinx 2)/?(x 2)/=cosx 2?(2x )=2x ?cosx 2
(14)f /=[ln (2x 2+6x )]/?(2x 2+6x)/ =
x 6x 212+? (4x+6) = x
3x 3x 22++
(15)f (x )=x 1x 3x 2++ = x+3+x 1 f /=(x+3+x 1)/= 1+0 -2x
1 =22x 1-x
(16)f /=(x )/(lnx )+(x )(lnx )/+9
=lnx+x
1x ?+9 =lnx+10
(17)f (x )=
x
sinx lnx + f /=2x
x sinx lnx -x sinx lnx )()()('?+?'+ =2x
1
sinx lnx -x cosx x 1?+?+)()( =2x
sinx lnx -cosx x 1)()(+?+ =2x
sinx lnx -cosx x 1-?+
(18)因为f (x )=tanx =cosx
sinx
所以:f /=(cosx sinx )/= 2cosx cosx sinx cosx sinx )
()()()()('?-?' =2cosx sinx sinx cosx cosx )()()(-?-? =222cosx sinx cosx )
()()(+ =2cosx 1)
( =sec 2x
(19)f (x )=x
x
e 1e 1-+
f /=2x x x x x e 1e 1e 1e 1e 1)
()()()()(-'-?+--?'+ =2x x x x x e 1e e 1e 1e )
()()()(--?+--? =2x x
e 12e )
(-
(20)f(x)=(x2-x)3
f/=3(x2-x)2(x2-x)/
=3x2(x-1)2(2x-1)