Calculus

$\displaystyle \frac{d}{dx}\,x^{\,n}$	$\displaystyle = n\,x^{\,n-1}$	(B.1)
$\displaystyle \frac{d}{dx}\,{\rm e}^x$	$\displaystyle = {\rm e}^x$	(B.2)
$\displaystyle \frac{d}{dx}\,\ln x$	$\displaystyle = \frac{1}{x}$	(B.3)
$\displaystyle \frac{d}{dx}\,\sin x$	$\displaystyle = \cos x$	(B.4)
$\displaystyle \frac{d}{dx}\,\cos x$	$\displaystyle = -\sin x$	(B.5)
$\displaystyle \frac{d}{dx}\,\tan x$	$\displaystyle = \frac{1}{\cos^2 x}$	(B.6)
$\displaystyle \frac{d}{dx}\,\sin^{-1} x$	$\displaystyle = \frac{1}{\sqrt{1-x^{\,2}}}$	(B.7)
$\displaystyle \frac{d}{dx}\,\cos^{-1} x$	$\displaystyle = -\frac{1}{\sqrt{1-x^{\,2}}}$	(B.8)
$\displaystyle \frac{d}{dx}\,\tan^{-1} x$	$\displaystyle = \frac{1}{1+x^{\,2}}$	(B.9)
$\displaystyle \frac{d}{dx}\,\sinh x$	$\displaystyle =\cosh x$	(B.10)
$\displaystyle \frac{d}{dx}\,\cosh x$	$\displaystyle = \sinh x$	(B.11)
$\displaystyle \frac{d}{dx}\,\tanh x$	$\displaystyle = \frac{1}{\cosh^2 x}$	(B.12)
$\displaystyle \frac{d}{dx}\,\sinh^{-1} x$	$\displaystyle = \frac{1}{\sqrt{x^{\,2}+1}}$	(B.13)

$\displaystyle \frac{d}{dx}\,\cosh^{-1} x$	$\displaystyle =\pm \frac{1}{\sqrt{x^{\,2}-1}}$	(B.14)
$\displaystyle \frac{d}{dx}\,\tanh^{-1} x$	$\displaystyle = \frac{1}{1-x^{\,2}}$	(B.15)