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Difference between revisions of "Derivative/Formulas"

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== List of formulas ==
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{| style="margin: 1em auto 1em auto; height:1000px"
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| <math>\frac d{dx}(cf(x)) = c\left(\frac d{dx} f(x)\right)</math> where c is a constant
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|-
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| <math>(f(x) + g(x))' = f'(x) + g'(x)</math>
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|-
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| <math>(f(x)-g(x))'=f'(x)-g'(x)</math>
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|-
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| <math>\left(u(x)\times v(x)\right)'=u(x)v'(x)+u'(x)v(x)</math>
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|-
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| <math>\left(\frac{u(x)}{v(x)}\right)' = \frac{u'(x)v(x) - u(x)v'(x)}{(v(x))^2}</math>
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|-
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| <math>(f(g(x)))' = f'(g(x))g'(x)</math>
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|-
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| <math>\frac d{dx} x^n = n x^{n-1}</math>
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|-
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| <math>\frac d{dx} (f(x))^n =n f(x)^{n-1} f'(x)</math>
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|-
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| <math>\frac d{dx} \sin x = \cos x</math>
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|-
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| <math>\frac d{dx} \cos x = -\sin x</math>
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|-
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| <math>\frac d{dx} \tan x = \sec^2 x</math>
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|-
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| <math>\frac d{dx} \sec x = \sec x \tan x</math>
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|-
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| <math>\frac d{dx} \csc x = -\csc x\cot x</math>
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|-
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| <math>\frac d{dx} \cot x = -\csc^2 x</math>
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|-
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| <math>\frac d{dx} e^x = e^x</math>
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|-
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| <math>\frac d{dx} a^x = (\ln a) a^x</math>
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|-
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| <math>\frac d{dx} \ln x = \frac 1x</math>
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|-
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| <math>\frac d{dx} \log_b x =\frac{\log_b e}{x} </math>
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|-
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| <math>\frac d{dx} \arcsin x = \frac 1{\sqrt{1-x^2}}</math>
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|-
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| <math>\frac d{dx} \arccos x = -\frac 1{\sqrt{1-x^2}}</math>
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|-
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| <math>\frac d{dx} \arctan x = \frac 1{1+x^2}</math>
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|-
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| <math>\frac d{dx} \mathrm{arcsec \ } x = \frac 1{\mid x \mid\sqrt{x^2-1}}</math>
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|-
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| <math>\frac d{dx} \mathrm{arccsc \ } x = - \frac 1{x\sqrt{x^2 - 1}}</math>
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|-
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| <math>\frac d{dx} \mathrm{arccot \ } x = - \frac 1{1+x^2}</math>
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|}
  
 
== See also ==
 
== See also ==
 
* [[Calculus]]
 
* [[Calculus]]
 
* [[Derivative]]
 
* [[Derivative]]

Revision as of 00:58, 27 March 2009

List of formulas

$\frac d{dx}(cf(x)) = c\left(\frac d{dx} f(x)\right)$ where c is a constant
$(f(x) + g(x))' = f'(x) + g'(x)$
$(f(x)-g(x))'=f'(x)-g'(x)$
$\left(u(x)\times v(x)\right)'=u(x)v'(x)+u'(x)v(x)$
$\left(\frac{u(x)}{v(x)}\right)' = \frac{u'(x)v(x) - u(x)v'(x)}{(v(x))^2}$
$(f(g(x)))' = f'(g(x))g'(x)$
$\frac d{dx} x^n = n x^{n-1}$
$\frac d{dx} (f(x))^n =n f(x)^{n-1} f'(x)$
$\frac d{dx} \sin x = \cos x$
$\frac d{dx} \cos x = -\sin x$
$\frac d{dx} \tan x = \sec^2 x$
$\frac d{dx} \sec x = \sec x \tan x$
$\frac d{dx} \csc x = -\csc x\cot x$
$\frac d{dx} \cot x = -\csc^2 x$
$\frac d{dx} e^x = e^x$
$\frac d{dx} a^x = (\ln a) a^x$
$\frac d{dx} \ln x = \frac 1x$
$\frac d{dx} \log_b x =\frac{\log_b e}{x}$
$\frac d{dx} \arcsin x = \frac 1{\sqrt{1-x^2}}$
$\frac d{dx} \arccos x = -\frac 1{\sqrt{1-x^2}}$
$\frac d{dx} \arctan x = \frac 1{1+x^2}$
$\frac d{dx} \mathrm{arcsec \ } x = \frac 1{\mid x \mid\sqrt{x^2-1}}$
$\frac d{dx} \mathrm{arccsc \ } x = - \frac 1{x\sqrt{x^2 - 1}}$
$\frac d{dx} \mathrm{arccot \ } x = - \frac 1{1+x^2}$

See also

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