下面7种基本求导公式要熟稔于心、倒背如流:

①:

(xμ)=μxμ1 (x^\mu)' = \mu x^{\mu-1}

②:

(ex)=ex (e^x)' = e^x

(ax)=axlna(a^x)' = a^xlna

③:

(lnx)=1x (lnx)' = \frac{1}{x}

(lnx)=1x (ln|x|)' = \frac{1}{x}

④:

(sinx)=cosx (sinx)' = cosx                    (cosx)=sinx (cosx)' = -sinx
(tanx)=sec2x (tanx)' = sec^2x                  (cotx)=csc2x (cotx)' = -csc^2x
(secx)=secxtanx (secx)' = secxtanx         (cscx)=cscxcotx (cscx)' = -cscxcotx

⑤:

(arctanx)=11+x2 (arctanx)' = \frac{1}{1+x^2}      (arccotx)=11+x2 (arccotx)' = -\frac{1}{1+x^2}

⑥:

(arcsinx)=11x2 (arcsinx)' = \frac{1}{\sqrt{1-x^2}}    (arccos)=11x2 (arccos)' = -\frac{1}{\sqrt{1-x^2}}

⑦:

(ln(x+x2+a2))=1x2+a2 (ln(x+\sqrt{x^2+a^2}))' = \frac{1}{\sqrt{x^2+a^2}}   常见的是a=1的情况: (ln(x+x2+1))=1x2+1 (ln(x+\sqrt{x^2+1}))' = \frac{1}{\sqrt{x^2+1}}

(ln(x+x2a2))=1x2a2 (ln(x+\sqrt{x^2-a^2}))' = \frac{1}{\sqrt{x^2-a^2}}   常见的是a=1的情况:(ln(x+x21))=1x21 (ln(x+\sqrt{x^2-1}))' = \frac{1}{\sqrt{x^2-1}}

补充常用的几个求导公式:

(1x)=1x2 (\frac{1}{x})' = -\frac{1}{x^2}

复合函数情况:

(u)=u2u(\sqrt{u})' = \frac{u'}{2\sqrt{u}}

文档更新时间: 2019-10-09 20:11   作者:数学公式