基礎(chǔ)知識整合
1.導(dǎo)數(shù)的概念
(1)f(x)在x=x0處的導(dǎo)數(shù)就是f(x)在x=x0處的瞬時變化率,記作:y′|x=x0或f′(x0),即f′(x0)= .
(2)當(dāng)把上式中的x0看作變量x時,f′(x)即為f(x)的導(dǎo)函數(shù),簡稱導(dǎo)數(shù),即y′=f′(x)= .
2.導(dǎo)數(shù)的幾何意義
函數(shù)f(x)在x=x0處的導(dǎo)數(shù)就是曲線y=f(x)在點P(x0,f(x0))處的切線的斜率,即曲線y=f(x)在點P(x0,f(x0))處的切線的斜率k=f′(x0),切線方程為y-y0=f′(x0)(x-x0).
3.基本初等函數(shù)的導(dǎo)數(shù)公式
(1)C′=0(C為常數(shù));
(2)(xn)′=nxn-1(n∈Q*);
(3)(sinx)′=cosx;(4)(cosx)′=-sinx;
(5)(ax)′=axln_a;(6)(ex)′=ex;
(7)(logax)′=;(8)(ln x)′=.
4.導(dǎo)數(shù)的運算法則
(1)[f(x)±g(x)]′=f′(x)±g′(x).
(2)[f(x)·g(x)]′=f′(x)g(x)+f(x)g′(x).
特別地:[C·f(x)]′=Cf′(x)(C為常數(shù)).