求导法则

2018-12-10 本文已影响0人一碗好吃的乌冬面

1.常数和基本初等函数的导数公式

1. $(C)' = 0$
2. $(x^n)' =\mu x^{n-1}$
3. $(\sin x)' =\cos x$
4. $(\cos x )' = - \sin x$
5. $(\tan x)' =\sec^2 x$
6. $(\cot x)' = - \csc^2 x$
7. $(\sec x)' = \sec x \tan x$
8. $(\csc x)' = - \csc x \cot x$
9. $(a^x)' = a^x \ln a$
10. $(e^x)' = e^x$
11. $(\log_ax)' = \frac{1}{x\ln a}$
12. $(\ln x)' = \frac{1}{x}$
13. $(\arcsin x)' = \frac{1}{\sqrt {1-x^2}}$
14. $(\arccos {x})' = -\frac{1}{\sqrt {1-x^2}}$
15. $(\arctan x)' = \frac{1}{1+x^2}$
16. $(\mathrm{arccot}\,x)' = -\frac{1}{1+x^2}$

2.函数的和，差，积，商，的求导法则

设 $u = u(x), v = v(x)$ 都可导，则

(1) $(u \pm v)' = u' \pm v'$ 　　　　　　(2) $(Cu)' = Cu'$ ( $C$ 是常数)
(3) $(uv)' = u'v + uv'$ 　　　　　　 (4) $\left (\frac{u}{v}\right)' = \frac{u'v - uv'}{v^2} (v\neq0)$