Question

設(shè)函數(shù)f（x）=1n（2-3x）⁵，則f′(

1

3

)=

 

．

Answer 1

分析：先利用復(fù)合函數(shù)的導(dǎo)數(shù)運(yùn)算法則及基本初等函數(shù)的導(dǎo)數(shù)公式求出f（x）的導(dǎo)數(shù)，再將導(dǎo)數(shù)中的x用

1

3

代替，求出值．

解答：解：∵f（x）=1n（2-3x）⁵
∴f′（x）=

1

(2-3x)5

×[(2-3x)5]′
=

1

(2-3x)5

×5(2-3x)4×(2-3x)′
=

-15

2-3x

∴f′(

1

3

)=-15
故答案為：-15．

點(diǎn)評(píng)：求函數(shù)在某一點(diǎn)處的導(dǎo)數(shù)值，應(yīng)該先利用導(dǎo)數(shù)的運(yùn)算法則及初等函數(shù)的導(dǎo)數(shù)公式求出導(dǎo)函數(shù)，再求導(dǎo)數(shù)值．