Calculus

$\displaystyle \frac{d}{dx}\,{\rm e}^x$	$\displaystyle = {\rm e}^x$	(A.1)
$\displaystyle \frac{d}{dx}\,\ln x$	$\displaystyle = \frac{1}{x}$	(A.2)
$\displaystyle \frac{d}{dx}\,\sin x$	$\displaystyle = \cos x$	(A.3)
$\displaystyle \frac{d}{dx}\,\cos x$	$\displaystyle = -\sin x$	(A.4)
$\displaystyle \frac{d}{dx}\,\tan x$	$\displaystyle = \frac{1}{\cos^2 x}$	(A.5)
$\displaystyle \frac{d}{dx}\,\sin^{-1} x$	$\displaystyle = \frac{1}{\sqrt{1-x^{\,2}}}$	(A.6)
$\displaystyle \frac{d}{dx}\,\cos^{-1} x$	$\displaystyle = -\frac{1}{\sqrt{1-x^{\,2}}}$	(A.7)
$\displaystyle \frac{d}{dx}\,\tan^{-1} x$	$\displaystyle = \frac{1}{1+x^{\,2}}$	(A.8)
$\displaystyle \frac{d}{dx}\,\sinh x$	$\displaystyle = \cosh x$	(A.9)
$\displaystyle \frac{d}{dx}\,\cosh x$	$\displaystyle = \sinh x$	(A.10)
$\displaystyle \frac{d}{dx}\,\tanh x$	$\displaystyle = \frac{1}{\cosh^2 x}$	(A.11)
$\displaystyle \frac{d}{dx}\,\sinh^{-1} x$	$\displaystyle = \frac{1}{\sqrt{1+x^{\,2}}}$	(A.12)
$\displaystyle \frac{d}{dx}\,\cosh^{-1} x$	$\displaystyle = \frac{1}{\sqrt{x^{\,2}-1}}$	(A.13)
$\displaystyle \frac{d}{dx}\,\tanh^{-1} x$	$\displaystyle = \frac{1}{1-x^{\,2}}$	(A.14)