next up previous
Next: Series expansions Up: Useful mathematics Previous: Useful mathematics

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)


next up previous
Next: Series expansions Up: Useful mathematics Previous: Useful mathematics
Richard Fitzpatrick 2016-03-31