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Calculus

$\displaystyle \frac{d}{dx}\,x^{\,n}$ $\displaystyle = n\,x^{\,n-1}$ (1211)
$\displaystyle \frac{d}{dx}\,{\rm e}^x$ $\displaystyle = {\rm e}^x$ (1212)
$\displaystyle \frac{d}{dx}\,\ln x$ $\displaystyle = \frac{1}{x}$ (1213)
$\displaystyle \frac{d}{dx}\,\sin x$ $\displaystyle = \cos x$ (1214)
$\displaystyle \frac{d}{dx}\,\cos x$ $\displaystyle = -\sin x$ (1215)
$\displaystyle \frac{d}{dx}\,\tan x$ $\displaystyle = \frac{1}{\cos^2 x}$ (1216)
$\displaystyle \frac{d}{dx}\,\sin^{-1} x$ $\displaystyle = \frac{1}{\sqrt{1-x^2}}$ (1217)
$\displaystyle \frac{d}{dx}\,\cos^{-1} x$ $\displaystyle = -\frac{1}{\sqrt{1-x^2}}$ (1218)
$\displaystyle \frac{d}{dx}\,\tan^{-1} x$ $\displaystyle = \frac{1}{1+x^2}$ (1219)
$\displaystyle \frac{d}{dx}\,\sinh x$ $\displaystyle =\cosh x$ (1220)
$\displaystyle \frac{d}{dx}\,\cosh x$ $\displaystyle = \sinh x$ (1221)
$\displaystyle \frac{d}{dx}\,\tanh x$ $\displaystyle = \frac{1}{\cosh^2 x}$ (1222)
$\displaystyle \frac{d}{dx}\,\sinh^{-1} x$ $\displaystyle = \frac{1}{\sqrt{x^2+1}}$ (1223)

$\displaystyle \frac{d}{dx}\,\cosh^{-1} x$ $\displaystyle =\pm \frac{1}{\sqrt{x^2-1}}$ (1224)
$\displaystyle \frac{d}{dx}\,\tanh^{-1} x$ $\displaystyle = \frac{1}{1-x^2}$ (1225)


next up previous
Next: Series Expansions Up: Useful Mathematics Previous: Useful Mathematics
Richard Fitzpatrick 2013-04-08