15 ちょっとまとめ

				$f^{(n)}(x)$
(定数)	0	0	0	0
$x^{\alpha}$	$\alpha x^{\alpha-1}$	$\alpha(\alpha-1) x^{\alpha-2}$	$\alpha(\alpha-1)(\alpha-2)x^{\alpha-3}$	$\displaystyle{\frac{\alpha!}{(\alpha-n)!}x^{\alpha-n}}$ ( $n\leq\alpha\in\mathbb{N}$ )
( $\alpha\in\mathbb{R}$ )				0 ( $n<\alpha\in\mathbb{N}$ )
				$\displaystyle{\frac{\alpha!}{(\alpha-n)!}x^{\alpha-n}}$ ( $\alpha\notin\mathbb{N}$ )
$\log x$	$\displaystyle{\frac{1}{x}}$
$\log_{a} x$	$\displaystyle{\frac{1}{(\log a)\,x}}$
$e^{x}$	$e^{x}$	$e^{x}$	$e^{x}$	$e^{x}$
$a^{x}$	$(\log a)\,a^{x}$	$(\log a)^2\,a^{x}$	$(\log a)^3\,a^{x}$	$(\log a)^{n}\,a^{x}$
$\sin x$	$\cos x$	$-\sin x$	$-\cos x$
$\cos x$	$-\sin x$	$-\cos x$	$\sin x$
$\tan x$	$\displaystyle{\frac{1}{\cos^2 x}}$
$\mathrm{Sin}^{-1} x$	$\displaystyle{\frac{1}{\sqrt{1-x^2}}}$
$\mathrm{Cos}^{-1} x$	$\displaystyle{\frac{-1}{\sqrt{1-x^2}}}$
$\mathrm{Tan}^{-1} x$	$\displaystyle{\frac{1}{1+x^2}}$
$\sinh x$	$\cosh x$	$\sinh x$	$\cosh x$
$\cosh x$	$\sinh x$	$\cosh x$	$\sinh x$
$\tanh x$	$\displaystyle{\frac{1}{\cosh^2 x}}$
$\sinh^{-1} x$	$\displaystyle{\frac{1}{\sqrt{x^2+1}}}$
$\mathrm{Cosh}^{-1} x$	$\displaystyle{\frac{1}{\sqrt{x^2-1}}}$
$\tanh^{-1} x$	$\displaystyle{\frac{1}{1-x^2}}$