2.1-.基本初等函数的导数公式及导数的运算法则ppt课件

1、资中县龙结中学数学组资中县龙结中学数学组(第三课时第三课时)资中县龙结中学数学组资中县龙结中学数学组一、基本初等函数的导数公式表一、基本初等函数的导数公式表为 常 数则则则则则则则则x xx xa a若若 f f ( ( x x ) ) = = c c ( ( c c) ) , ,f f ( ( x x ) ) = =若若 f f ( ( x x ) ) = = x x ( (Q Q ) ) , ,f f ( ( x x ) ) = =若若 f f ( ( x x ) ) = = s s i i n n x x , ,f f ( ( x x ) ) = =若若 f f ( ( x x ) )

2、= = c c o o s s x x , ,f f ( ( x x ) ) = =若若 f f ( ( x x ) ) = = a a , ,f f ( ( x x ) ) = =若若 f f ( ( x x ) ) = = e e , ,f f ( ( x x ) ) = =若若 f f ( ( x x ) ) = = l l o o g g x x , ,f f ( ( x x ) ) = =若若 f f ( ( x x1 1 . .2 2 . .3 3 . .4 4 . .5 5 . .6 6 . .) ) = = l l n n x x , ,f f7 7 . .8 8 . .( (

3、 x x ) ) = =0 0 - -1 1 x xcosxcosx-sinx-sinxlnax xa aexex1 1x xl ln na a1 1x x资中县龙结中学数学组资中县龙结中学数学组二、导数的运算法则二、导数的运算法则f f( (x x) ) 1 1g g( (x x) ). .= = f f( (x x) )2 2g g( (x x) ). .= =f f( (x x) ) = = ( (g g g g( (x x) )3 3. .( (x x) )0 0) )别为数c cg g( (x x) ) = = 特特地地( (c c 常常 ) )f f( (x x) )g g( (x

4、 x) )f f( (x x) )g g( (x x) )+ +f f( (x x) )g g( (x x) )gc c ( (x x) )2 2f f( (x x) )g g( (x x) )- -f f( (x x) )g g( (x x) )g g( (x x) )资中县龙结中学数学组资中县龙结中学数学组 设函数设函数 在点在点x处有导数处有导数 ,函数函数y=f(u)在点在点x的对应点的对应点u处有导数处有导数 ,则复合则复合函数函数 在点在点x处也有导数处也有导数,且且 或记或记)(xu )(xux )(ufyu ;xuxuyy ).()()(xufxfx )(xfy 求复合函数的导

5、数求复合函数的导数,关键在于分清函数的复合关键在于分清函数的复合关系关系,合理选定中间变量合理选定中间变量,明确求导过程中每次是明确求导过程中每次是哪个变量对哪个变量求导哪个变量对哪个变量求导,一般地一般地,如果所设中间如果所设中间变量可直接求导变量可直接求导,就不必再选中间变量就不必再选中间变量.三、复合函数的导数三、复合函数的导数资中县龙结中学数学组资中县龙结中学数学组例例1 1 求下列函数的导数求下列函数的导数: :2 2x x( (1 1) )y y = =3 3x x - -4 4x x+ +8 8 ( (2 2) )y y = =x xc co os sx x- -s si in

6、nx x1 1l ln nx x( (3 3) )y y = =x xe e - - ( (4 4) )y y = =+ +c co os sx xx xx x解解:(1):(1)(2)(2)(3)(3)(4)(4)y=6x-4y=-xsinx3212x3212xy=ex+xex+3 3- -2 21 1x x2 22 21-lnx1-lnx-sinx-sinxx xy=2 21 1 - -l ln nx x- - s si in nx xx x资中县龙结中学数学组资中县龙结中学数学组解解:(1):(1)(2)(2)(3)(3)(4)(4)5 51 12 2y y = =1 1- - 3 3x x2 24 4x x+ +1 1y y = =2 2x x + + x x3 3x x- -1 1y y = =2 2x x- -1 1资