ちょっとまとめ

$f(x)$	$f'(x)$	$f''(x)$	$f'''(x)$	$f^{(n)}(x)$
$c$ (定数)	0	0	0	0
$x^{\alpha}$	$\alpha x^{\alpha-1}$	$\alpha(\alpha-1) x^{\alpha-2}$	$\alpha(\alpha-1)(\alpha-2)x^{\alpha-3}$	$${\frac{\alpha!}{(\alpha-n)!}x^{\alpha-n}}$$     ( $n\leq\alpha\in\mathbb{N}$)
( $\alpha\in\mathbb{R}$)				0     ( $n<\alpha\in\mathbb{N}$)
				$${\frac{\alpha!}{(\alpha-n)!}x^{\alpha-n}}$$     ( $\alpha\notin\mathbb{N}$)
$\log x$	$${\frac{1}{x}}$$
$\log_{a} x$	$${\frac{1}{(\log a)\,x}}$$
$e^{x}$	$e^{x}$	$e^{x}$	$e^{x}$	$e^{x}$
$a^{x}$	$(\log a)\,a^{x}$	$(\log a)^2\,a^{x}$	$(\log a)^3\,a^{x}$	$(\log a)^{n}\,a^{x}$
$\sin x$	$\cos x$	$-\sin x$	$-\cos x$
$\cos x$	$-\sin x$	$-\cos x$	$\sin x$
$\tan x$	$${\frac{1}{\cos^2 x}}$$
$\arcsin x$	$${\frac{1}{\sqrt{1-x^2}}}$$
$\arccos x$	$${\frac{-1}{\sqrt{1-x^2}}}$$
$\arctan x$	$${\frac{1}{1+x^2}}$$
$\sinh x$	$\cosh x$	$\sinh x$	$\cosh x$
$\cosh x$	$\sinh x$	$\cosh x$	$\sinh x$
$\tanh x$	$${\frac{1}{\cosh^2 x}}$$
$\mathrm{arcsinh}\,x$	$${\frac{1}{\sqrt{x^2+1}}}$$
$\mathrm{arccosh}\,x$	$${\frac{1}{\sqrt{x^2-1}}}$$
$\mathrm{arctanh}\,x$	$${\frac{1}{1-x^2}}$$

問 3.40   上の表の空いている個所を埋めよ．

Kondo Koichi
Created at 2002/09/12